Let that number be variable x
MATHEMATICALLY THE STATEMENT IS SAYING
[tex]8x + 3 = 19 \\ 8x = 19 - 3 \\ 8x = 16 \\ \frac{8x}{8} = \frac{16}{8} \\ x = 2 [/tex]
That number is 2ATTACHED IS THE SOLUTION
7TH GRADE MATH, BRAINLIEST WILL BE AWARDED
Answers:
Q1.a: 11g
Q1.b: 3m
Q1.3: [tex]-k^{2}[/tex]
Q2.a: 8x + 11y
Q2.b: 2a + b - 2c
Q3.a: 5q + 7
Q3.b: 6r + 3s + 7t
Step-by-step explanation:
Q1) simplify each of these expressions:
a. [tex]4g + 6g + g[/tex]
= g(4 + 6 + 1)
= 11g
____________
b. [tex]4m - m[/tex]
= m(4 - 1)
= 3m
____________
c. [tex]5k^{2} -4k^{2} -2k^{2}[/tex]
= [tex]k^{2} (5 - 4 - 2)\\[/tex]
= [tex]-1k^{2}[/tex]
= [tex]-k^{2}[/tex]
__________________________________
Q2) copy and complete the workings to simplify these expressions:
a. [tex]5x + 3x+6y+5y\\[/tex]
= x(5 + 3) + y(6 + 5)
= 8x + 11y
____________
b.[tex]2a+4b+6c-3b-8c[/tex]
combine terms b:
2a + b + 6c - 8c
combine terms c:
= 2a + b - 2c
__________________________________
Q3) simplify these expressions by collecting like terms:
a.[tex]9q-4q+15-8[/tex]
combine terms q:
5q + 15 - 8
combine numbers:
= 5q + 7
____________
b. [tex]8r+2s+4t-2r+s+3t[/tex]
combine terms r:
6r + 2s + 4t + s + 3t
combine terms s:
6r + 3s + 4t + 3t
combine terms t:
= 6r + 3s + 7t
For the following inequality, choose their equivalent interval notation. A) 0_
Recall that the symbols ≤ and ≥ in interval notation are represented by ] and [ respectively.
Also, the symbols < and > in interval notation are represented by ) and ( respectively.
Therefore:
a)
[tex]0\le x\le1[/tex]in interval notation is:
[tex]\lbrack0,1\rbrack\text{.}[/tex]b)
[tex]0in interval notation is:[tex](0,4)\text{.}[/tex]Answer:
a)
[tex]\lbrack0,1\rbrack\text{.}[/tex]b)
[tex](0,4)[/tex]If tan thita= 1/(root3) , then sin thita =? answer should be 1/2 according to book. please give solve
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A cake of mass 550 g has three dry ingredients: flour, sugar and raisins.
There is twice as much flour as sugar and one and a half times as much
sugar as raisins. How much flour is there?
Answer:
Let flour, sugar, raisins be 3x, 1.5x, x grams respectively.
Total Mass = 550g 3x+1.5x + x = 550g
5.5x = 550 x = 100g
Flour = 3x= 3 x 100 = 300g
Hence, flour in mixture is 300g
- 1/2 + 5/9 someone help
everything u need id in the picture
Calculate the mean height of five men whose weight in kg are 60, 65, 71, 75 and 80
Answer:
Given the data set of height (inches) for 12 students, calculate the mean: 60, 64, 66, 68, 70, 71, 72, 73, 78, 71, 65, 69
Suppose a diver jumps from a ledge that is 115 feet above the ocean and the initial upward velocity is 8 feet per second. The vertical motion of the diver can be modeled by the function h = −t^2 + 8t + 115. How long will it take until the diver enters the water? How do you know?
The given function of the height of the diver is
[tex]h=-t^2+8t+115[/tex]h is the height in feet
t is the time in seconds
To find the time for the whole motion equate h by 0, as when the diver inter the water his jumper height will be zero. (The surface of the water is the initial position)
[tex]0=-t^2+8t+115[/tex]Switch the 2 sides and change all signs to opposite
[tex]t^2-8t-115=0[/tex]Now, we have a quadratic equation, then we will use the calculator to find the values of t
[tex]\begin{gathered} t=15.44552314 \\ \\ t=-7.445523142 \end{gathered}[/tex]Since time can NOT be a negative value, then we will ignore the 2nd value of t
The answer should be about 15.44 seconds to the nearest 2 decimal place
What is the product of 3x^2 and 2x^3y+5xy^4 ?
The product of two expressions can be calculated using distributive property as,
[tex](2x^3y+5xy^4)(3x^2)=2x^3y\times3x^2+5xy^4\times3x^2[/tex](Distributive property (A+B)C=AC+BC) )
[tex]\begin{gathered} (2x^3y+5xy^4)(3x^2)=6x^{3+2}y+15x^{1+2}y^4 \\ =6x^5y+15x^3y^4 \end{gathered}[/tex]Therefore, the product of the expressions is,
[tex]6x^5y+15x^3y^4[/tex]hello can you help me to understand this. 4 (18) it's 2 dots (19) 3 dots (20) 6 dots (21) 4 dots (22) 1 dots (23) 1 dot (24) ??? I don't get it
Explanation
to plot this, you need to count the numbers of weigth for that number, for example
for 18
count in the table all the 18
you will get 18 is 2 times in the table (2)
now, for 19
count the number of 19's in the table 3
and so on
Step 1
then, for 24
total = 0
so, as we have not 24 as a data, there is not need to plot it
I hope this helps you
3 11 / 16 simplified
Multiply the full number by the denominator to convert a mixed number to an improper fraction. If the value be 3 11 / 16 then simplifying the value 59 / 16.
How to convert mixed numbers to improper fraction?Multiply the full number by the denominator to convert a mixed number to an improper fraction. Include it in the numerator. Add that total to the denominator from the beginning.
To make a mixed number from an improper fraction, divide the numerator by the denominator. After division, the mixed number is produced in such a way that the obtained quotient becomes the entire number, the remainder becomes the new numerator, and the denominator remains constant.
Let the value be 3 11 / 16
Convert mixed numbers to improper fraction: [tex]$a \frac{b}{c}=\frac{a \cdot c+b}{c}$[/tex]
[tex]$&3 \frac{11}{16}=\frac{3 \cdot 16+11}{16}=\frac{59}{16} \\[/tex]
= 59 / 16
Therefore, the correct answer is 59 / 16.
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Tan theta=10
Find sin(2theta)+cos(2theta)
Answer: B
Step-by-step explanation:
[tex]\tan \theta=10 \implies \sin \theta=\frac{10}{\sqrt{101}}, \cos \theta=\frac{1}{\sqrt{101}}[/tex]
[tex]\sin 2\theta=2\sin \theta \cos \theta=2 \left(\frac{10}{\sqrt{101}} \right)\left(\frac{1}{\sqrt{101}} \right)=\frac{20}{101}[/tex]
[tex]\cos 2\theta=2\cos^2 \theta-1=2 \left(\frac{1}{\sqrt{101}} \right)^2 -1=-\frac{99}{101}[/tex]
[tex]\therefore \sin 2\theta+\cos 2\theta=\frac{20}[101}-\frac{99}{101}=-\frac{79}{101}[/tex]
Tiana invests $83,927 in a start-up company. She will be repaid at the end of 7 years at 7% interest compounded annually. Find the amount of interest she willearn on this investment.DO NOT ROUND ANY NUMBERS UNTIL YOUR FINAL ANSWER!Round to the nearest dollar.
For a initial amount invested P at a annual interest rate r, the total amount after n years is given by:
[tex]A=P\cdot(1+r)^n[/tex]For P = $83927, r = 0.07 and n = 7, we have:
[tex]\begin{gathered} A=83927\cdot1.07^7 \\ A=\text{ \$134768.422} \end{gathered}[/tex]Then, the amount of interest Tiana will earn on this investment is given by:
[tex]A-P=134768.422-83927=\text{ \$50841}[/tex]Writing out and solving inequalities a number divided by three less two is at most two
The inequlaity is ;
[tex]\begin{gathered} \frac{x}{3\text{ }}\text{ - 2}\leq2 \\ \end{gathered}[/tex]
And the solution is;
[tex]x\text{ }\leq\text{ 12}[/tex]
Let the number be x
The number divided by 3
That is x/3
less two means minus 2
x/3 - 2
Is at most 2 means it is less than or equal to 2
so the inequality is;
[tex]\begin{gathered} \frac{x}{3}\text{ - 2}\leq\text{ 2} \\ \\ \text{Solving the inequality, we have} \\ \\ \frac{x}{3}\text{ }\leq\text{ 2 + 2} \\ \\ \frac{x}{3}\text{ }\leq\text{ 4} \\ \\ x\text{ }\leq\text{ 3 }\times\text{ 4 } \\ x\text{ }\leq\text{ 12} \end{gathered}[/tex]If the function h(x)=(x+7)9 is expressed in the form f∘g with f(x)=x9, find the function g(x).
Answer:
g(x) = x + 7
Step-by-step explanation:
f(x) = x^9
g(x) = x + 7
f(g(x)) = (x + 7)^9
Look at the figure below:If siny - and tan yo =9-what is the value of cos yº? O cos y 90cos yOcos yO cos y® - 90
The trigonometric functions tangent, sine and cosine are related by the following equation:
[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]In this case, the angle is y°, so:
[tex]\tan y\degree=\frac{\sin y\degree}{\cos y\degree}[/tex]Since we want the cosine, we can solve for it ans substitute the given tangent and sine:
[tex]\cos y\degree=\frac{\sin y\degree}{\tan y\degree}=\frac{\frac{9}{c}}{\frac{9}{d}}=\frac{9}{c}\cdot\frac{d}{9}=\frac{d}{c}[/tex]This corresponds to the third alternative.
What would be the first step when solving using the substitution method?
2x + 3y = -12
x = 3y + 3
The first step of substitution method for given system is put x = 3y +3 in place of x into the equation 2x+3y=-12 .
What is the method of substitution for system of equation in two variables ?The system of the equations in two variables x and y consists of two equation of the form a₁ x + b₁ y = c₁
and a₂ x + b₂ y = c₂
where a₁, a₂, b₁, b₂ , c₁, c₂ are constants
For substitution method, first expression of one variable is found from one equation and then put this expression in another equation to create a linear equation in second variable. Solve the linear equation in one variable for second variable and then put the value of second variable in first equation to solve for first variable
Given system of equations is :
2x + 3y = -12 .....(1)
x = 3y + 3 .....(2)
So the first step will be take expression for one variable from one equation and put it into another equation.
Take x = 3y +3 which is an expression for x from equation (2),
Then put it into equation (1)
⇒ 2 (3y +3 ) + 3 y = -12 , This is the first step of substitution method for this variable
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First find the term that should be added so that the expression is a perfect-square trinomial. w² + 7w + ___Then factor the trinomial.(___)²
to do a perfect-square trinomial the third term must be the square of the half of the second term
the sencond term is 7,so
[tex](\frac{7}{2})^2=\frac{49}{4}[/tex]so the expresion is
[tex]w^2+7w+\frac{49}{4}[/tex]and the factor
[tex](w+\frac{7}{2})^2[/tex]An example
[tex]w^2+\frac{8}{5}w+\cdots_{}[/tex]the third term is
[tex]\begin{gathered} (\frac{\frac{8}{5}}{2})^2 \\ \\ (\frac{4}{5})^2 \\ \\ =\frac{16}{25} \end{gathered}[/tex]so the percet-square is
[tex]w^2+\frac{8}{5}w+\frac{16}{25}[/tex]The equation y = - 50x + 2000 represents thenumber of people attending a movie where xrepresents the number of weeks since the movierelease and y represents the number of people inthe theater.In the equation, what does the y-interceptindicate?A. Two thousand people attend the theater duringthe week of a movie's release.B. Every week 50 less people attend the movietheater.C. During a movie's release week, the movietheater will make $2,000.D. Every week the movie is open, the movie theaterloses $50.
two thousand people attend the theater during the week of a movie's release (option A)
Explanation:The equation:
y = -50x + 2000
y = number of people in the theater
x = number of weeks since the movie release
2000 will be the number of people in the theater at the begining of the movie release
y-intercept of an equation represent the value of y when x is zero
The 2000 is the number of people in the theater at week zero.
Hence, y-intercept indicate two thousand people attend the theater during the week of a movie's release (option A)
Using the midpoint and distance formulas, calculate the coordinate of the midpoint and the length of the segment.
The midpoint formula [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex] and the length of coordinates can be determined from the formula [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
What are coordinates?
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane.
The x-axis & y-axis are the two axes that make up a coordinate plane (vertical).
The coordinates of the origin, which is the location where the two axes connect, are (0, 0).
The following formula is used to determine the separation between two coordinates :
The midpoint formula [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex] and the length of coordinates can be determined from the formula [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
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The midpoint of AB is at ( – 5, 4). If A = (0, – 9), find B.
Point of B is ( -10 , 0) is midpoint of AB .
What is midpoint of a segment?
The midpoint of a vertical line is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equal to the distance from both of them. It cuts the section in half.A midpoint is the position that is in the middle or center of a line connecting two points, often referred to as endpoints. The midpoint formula can be used to determine the other midpoint given one endpoint and a midpoint.The midpoint of AB = ( – 5, 4) = ( x ,y)
A = (0, – 9) ⇒ ( x₁ , y₁)
Let B = ( x₂, y₂ )
midpoint of AB ⇒ x = x₁ + x₂/2 , y = y₁ + y₂/2
-5 = 0 + x₂/2 , -9 = -9 + y₂/2
x₂ = -10 , y₂ = 0
point of B is ( -10 , 0)
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A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4,-1,7) and B is the point (16,-10,10). Find the coordinates of C.
We will solve as follows:
First: We will use the i, j, k vector notation to describe each point as a vector:
[tex]A=4i-j+7k[/tex][tex]B=16i-10j+10k[/tex]Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).
Second: We determine the speed from A to B:
[tex]v=\frac{B-A}{t_1}\Rightarrow v=\frac{(16-4)i+(-10+1)j+(10-7)k}{3}[/tex][tex]\Rightarrow v=\frac{12i-9j+3k}{3}\Rightarrow v=4i-3j+k[/tex]Third: We now determine the value of C:
[tex]C=B+vt_2\Rightarrow C=(16+4)i+(-10-3)j+(10+1)k[/tex][tex]\Rightarrow C=20i-13j+11k[/tex]So, we would have that the coordinates of C are:
[tex]C=(20,-13,11)[/tex](c) The total amount paid for a banquet, including gratuities of one-twentieth of the price
quoted for the banquet, was $2457. How
much of the amount paid was gratuities?
the amount paid for gatuities which 5 percent of the cost of banquet is
How to work out percentages?A percentage refers to a specific number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%.". The cost of gratuities is 1/20 or 5 percent of the amount paid for banquet. let us assume that x is the amount paid for banquet so
2457 is 120 percent of x
or 2457= [tex]\frac{120}{100}[/tex]×x
which implies x=2457×[tex]\frac{100}{120}[/tex]
x=2047.5$
this is the amount of banquet. to get the cost of gratuities we subtract this amount from the total cost.
amount paid for gratuities is 2457-2047.5=409.5$
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What is the place value of the 6-digit in the number 205.876?
The place value of 6 in 205.876 is 6 thousandth
Given: GC bisects FGH. Determine the missing measurea. m
a. Since GC bisects FGH and the angle FGH = 122°, we know that the angle FGC = 122/2 = 61°
b. Since GC bisects FGH and the angle CGH = 42°, we know that the angle FGH = 2*42 = 84°
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What is the solution to the given equation?
x= 20
How is the equation in the bar diagram solved?
3.5x + 12.5x =320
16x = 320
x = 20
What is a bar diagram?
A bar graph or chart displays categorical data using rectangular bars with heights or lengths proportional to the values they represent.Both vertical and horizontal plots of the bars are possible. Column charts are another name for vertical bar charts. Comparisons between distinct categories are shown in a bar graph. The chart's two axes, one for measured value and the other for the specified categories under comparison, are shown. In certain bar graphs, clusters of multiple bars that represent the values of multiple measured variables are clustered together.To learn more about solving equations, refer:
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The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time 3.25 minutes.
Main Answer: The probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is 0.59375.
Explaination:
Calculation of the probability:
Since The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes.
So, here the probability is
= 0.59375
Hence, The probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is 0.59375
The probability of a student eating at the cafeteria and a student living off campus is 0.07, and the probability of a student eating at the cafeteria given that the student lives off campus is 0.20, what is the probability of a student living off campus?
The probability of a student living off campus is 0.35.
What is the probability?It should be noted that probability simply means the likelihood that something will occur.
Remember the multiplication rule for conditional probability: P(B AND A)=P(B/A)P(A)
Rearranging, we find that P(A)=P(B AND A)P(B/A)
So if we think of A= the event a student lives off campus and B = event a student eats at the cafeteria, then we can plug in the known information to find:
P(A)=0.07 / 0.20
= 0.35
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After making your 20th payment of $524.50 on your car loan, you wanted to find out how much is left of your original 5 years loan at 6.2% compounded monthly of $27,000.00. What is the amount of the remaining balance of your car loan?
The amount of the remaining balance of the car loan is $26293.1103.
Given,
The initial loan amount, P = 27000
The rate of interest, r = 6.2%
Time period, t = 5 years
Interest is compounded monthly.
The 20th payment of the loan = $524.50
We have to find the remaining balance of the car loan.
Here,
Amount, A = P[1 + r/n]^nt
Where,
A is the total amount = principal amount + compound interest
P is the principal amount
r is the rate of interest
n is the number of times compounded
t is the time period
So,
A = P[1 + r/n]^nt
A = 27000 × [1 + 6.2/100/12]^12 × 5
A = 27000 × [12.062/12]^60
A = 27000 × [1.005166]^60
A = 27000 × 1.362
A = 36783.1103
The total amount should be paid after 60 months is $36783.1103
Now,
The 20th payment = $524.50
That is,
524.20 × 20 = 10490
$10490 is paid and the balance amount;
36783.1103 - 10490 = 26293.1103
Therefore,
The amount of the remaining balance of the car loan is $26293.1103.
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According to the graph, what is the temperature at the beginning of the year85 degrees60 degrees38 degrees0 degrees
From the graph
the curve start from a point close to 40
Hence at the beginning of the year January, the teperature was 38 degree
1936 divided by 8 in long division
The value of 1936 divided by 8 in long division is 242.
What is long division?Long Division is a method for dividing large numbers that divides the task into numerous phases that follow a sequence. Just like in conventional division problems, the dividend is divided by the divisor, yielding the quotient and, in some cases, a remainder.
The steps are:
Step 1: Take the first digit of the dividend from the left.
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend
Using the above step the division is 242.
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