We will have the following:
First, we solve both expressions for "y", that is:
[tex]\begin{gathered} 3x-7y=-4\Rightarrow-7y=-3x-4 \\ \Rightarrow y=\frac{3}{7}x+\frac{4}{7} \\ \\ and \\ \\ 2x-5y=-3\Rightarrow-5y=-2x-3 \\ \Rightarrow y=\frac{2}{5}x+\frac{3}{5} \end{gathered}[/tex]Now, we equal both expressions:
[tex]\begin{gathered} \frac{3}{7}x+\frac{4}{7}=\frac{2}{5}x+\frac{3}{5}\Rightarrow\frac{1}{35}x=\frac{1}{35} \\ \\ \Rightarrow x=1 \end{gathered}[/tex]Now, we determine the value of y:
[tex]y=\frac{2}{5}(1)+\frac{3}{5}\Rightarrow y=1[/tex]So, the solution is:
[tex](1,1)[/tex]Convert the following measurement 19 quarts to cups
76 cups
Explanation:Note that:
1 quart = 4 cups
Therefore:
19 quarts = 4 x 19 cups
19 quarts = 76 cups
Identify the key features for the following equation: y=4sin(x)−5What kind of cyclic model is the equation?
Given,
The equation of the function is:
[tex]y=4sinx-5[/tex]The standard equation of wave is,
[tex]y=Asin\text{ \lparen Bx+C\rparen+D}[/tex]Here, A is the amplitude
B is the period.
C is the phase shift.
D is vertical shift.
As the given function have the sine function so, the cyclic model of the wave is sine.
Amplitude = 4.
Midline = -5
Minimum = -9
Hence, the key feature of the cyclic model is identified.
What is the linear equation ( slope intercept equation ) for the line that passes through points (0,4) and (2,8) ?
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
Consideing the given points,
x1 = 0, y1 = 4
x2 = 2, y2 = 8
m = (8 - 4)/(2 - 0) = 4/2
m = 2
We would find the y intercept, c by substituting m = 2, x = 0 and y = 4 into the slope intercept equation. It becomes
4 = 2 * 0 + c
c = 4
Substituting m = 2 and c = 4 into the slope intercept equation, it becomes
y = 2x + 4
The last option is correct
solving absolute value inequalities[tex]8 - 9 |6x - 10| \ \textgreater \ - 82[/tex]please help with steps, I keep getting stuck on this one
For (1):
[tex]\begin{gathered} 6x-10<82 \\ \text{Add 10 to both sides:} \\ 6x<82+10 \\ 6x<92 \\ \text{Divide both sides by 6:} \\ x<\frac{92}{6} \\ x<\frac{46}{3} \\ \end{gathered}[/tex]For (2):
[tex]\begin{gathered} 6x-10>-82 \\ \text{Add 10 to both sides:} \\ 6x>-82+10 \\ 6x>-72 \\ \text{Divide both sides by 6:} \\ x>-\frac{72}{6} \\ x>-12 \end{gathered}[/tex]Therefore, the solution is:
[tex]-1269 is _________% more than 60
To find the solution we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 69\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{69\cdot100}{60} \\ x=115 \end{gathered}[/tex]This means that 69 is 115% of 60.
Therefore 69 is 15% more than 60.
find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer to 22.5 in
Semicrcle area = π•Diameter^2 / 8
. = 3.14 • (2 R)^2/8
. = 3.14• (45)^2/8
. = 3.14• 2025/8= 794.81
Then answer is
Area of semicircle = 795 square inches
how do you find 18.84 20.91 19.5 on a number line 14-22
In order to find the given numbers on a number line thats moves between 14 and 22, we shall illustrate with a number line.
The number line illustrated above shows the numbers arranged in order from 14 to 22.
The numbers indicated in the question are printed in blue.
The position of the numbers are also indicated with a black "stroke" in relation to the position of the numbers 14 to 22.
A vase can be modeled using x squared over 6 and twenty five hundredths minus quantity y minus 4 end quantity squared over 56 and 77 hundredths equals 1 and the x-axis, for 0 ≤ y ≤ 20, where the measurements are in inches. Using the graph, what is the distance across the base of the vase, and how does it relate to the hyperbola? Round the answer to the hundredths place.
We are given that a vase is modeled by the following hyperbola:
[tex]\frac{x^{2}}{6.25}-\frac{\left(y-4\right)^{2}}{56.77}=1[/tex]we are asked to determine the distance across the base. To do that we will first look at the graph of the equation:
Therefore, the base of the vase is the distance between the x-intercepts of the graph. To determine the x-intercepts we will set y = 0 in the equation. We get:
[tex]\frac{x^2}{6.25}-\frac{(0-4)^2}{56.77}=1[/tex]Solving the operation on the parenthesis we get:
[tex]\frac{x^2}{6.25}-\frac{16}{56.77}=1[/tex]Now we solve the fraction:
[tex]\frac{x^2}{6.25}-0.28=1[/tex]Now we add 0.28 to both sides:
[tex]\begin{gathered} \frac{x^2}{6.25}=1+0.25 \\ \\ \frac{x^2}{6.25}=1.25 \end{gathered}[/tex]Now we will multiply 6.25:
[tex]\begin{gathered} x^2=1.25(6.25) \\ x^2=7.81 \end{gathered}[/tex]Taking square root to both sides:
[tex]\begin{gathered} x=\sqrt[]{7.81} \\ x=\pm2.8 \end{gathered}[/tex]Therefore, the x-intercepts are -2.8 and 2.8.
Now we need to determine the distance between these two points. We will use the distance between two points in a line:
[tex]d=\lvert x_2-x_1\rvert[/tex]Substituting the points we get:
[tex]d=\lvert2.8-(-2.8)\rvert=\lvert2.8+2.8\rvert=5.6[/tex]Therefore, the distance is 5.6 inches and is related to the hyperbola in the sense that it is the distance between the x-intercepts.
How many solutions does the following system of equation have y = 2 x + 22y = 4x + 4
How many solutions does the following system of equation have
y = 2 x + 2
2y = 4x + 4
The answer is : Infinitely many solutions ( because they lie on each other ).
what is 4 2/3 + 7/9 as a fraction
The calculation is
[tex]4\cdot\frac{2}{3}+\frac{7}{9}[/tex]First step is to solve the multiplication.
4 means that there are four wholes, if you express in in thirds
[tex]\begin{gathered} 1\text{whole}=\frac{3}{3} \\ 4\text{wholes}=\frac{3\cdot4}{3}=\frac{12}{3} \end{gathered}[/tex]Then the multiplication you have to do is
[tex]\frac{12}{3}\cdot\frac{2}{3}=\frac{8}{3}[/tex]Now that the multiplication is done add 7/9
[tex]\frac{8}{3}+\frac{7}{9}=\frac{31}{9}[/tex]simplify (6r+5)(r-8)
To solve, first open the parenthesis
6r(r-8) + 5(r-8)
6r² - 48r + 5r - 40
Re-arrange
6r² + 5r -48r-40
6r² -43r - 40
Find the slope from the tableA. 3B. 2C. -3D. -1
Use 2 of the given ordered pairs to find the slope of the function. Use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where y2 and y1 are the y coordinates of the ordered pairs and x2 and x1 are the x coordinates. Replace for the given values:
[tex]m=\frac{2-5}{-2-(-3)}=-\frac{3}{1}=-3[/tex]The slope of the function is -3.
Find a recursive rule for the nth term of the sequence.7, 28, 112, 448, ...
Solution
Given the sequence 7, 28, 112, 448, ...
The sequence is a Geometric sequence because it has a common ratio
[tex]Common\text{ ratio, r = }\frac{28}{7}=4[/tex]First term, a = 4
[tex]\begin{gathered} The\text{ nth term of a gp = ar}^{n-1} \\ Where\text{ n=number of terms} \\ a=\text{ first term } \\ r=common\text{ ratio} \end{gathered}[/tex][tex]T_n=7\text{ \lparen4\rparen}^{n-1}[/tex][tex]\begin{gathered} For\text{ recursive, } \\ T_n=r.T_{n-1} \\ T_n=4(T_{n-1}) \end{gathered}[/tex][tex]The\text{ recursive rule is 4\lparen T}_{n-1})[/tex]Aiden ipens a savings account with a deposit of 4500. The account pays 3% simple interest.3. If Aiden does not make any more deposits or withdrawals, how much will he have in the account at the end of two years?A 4527B 4635C 4680D 4774E 4905
Answer: $4, 770
Aiden deposit $4500 into her account with an interest rate of 3%
Time = 2 years
Using the Simple Interest
[tex]\begin{gathered} I\text{ = }\frac{P\text{ x R x T}}{100} \\ P\text{ = \$4500} \\ R\text{ = 3\%} \\ T\text{ = 2} \\ I\text{ = }\frac{4500\text{ x 3 x 2}}{100} \\ I\text{ = }\frac{4500\text{ x 6}}{100} \\ I\text{ = }\frac{27000}{100} \\ I\text{ = \$270} \\ \text{The total amount in her account is } \\ \text{Balance = Principal + Interest} \\ \text{Balance = \$4500 + \$270} \\ \text{Balance = \$4, 770} \end{gathered}[/tex]Given:• 1 cm^3= 1 mL• 1 dm^3 = 1 L• 1L = 1,000 mLIf a health person's kidneys can filter 125 mL of blood per minute, then how long will it take for the kidneys to filter 4.5 L of blood?
Charnaie owns her own tutoring service. She charges new clients $20 for a placement test and then $10 per hour for every hour of tutoring.
Drag and drop the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
What is the independent variable in this real-world situation? Explain your reasoning.
The independent variable is the Response area because Response area.
What is the dependent variable in the real-world situation? Explain your reasoning.
The dependent variable is the Response area because Response area.
The correct equation for the given condition will be;
⇒ T = $20 + $10h
Where, T is the total cost and 'h' is the number of hours.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
She charges new clients $20 for a placement test and $10 per hour for every hour of tutoring.
Now,
Let total cost of charge = T
And, Number of hours = h
So, We can formulate by the given condition as;
⇒ T = $20 + $10h
Thus, The correct equation for the given condition will be;
⇒ T = $20 + $10h
Where, T is the total cost and 'h' is the number of hours.
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-2. The sum of two cubes can be factored by using the formula o’ + b3 (a + b)(c? ab + b?).(a) Verify the formula by multiplying the right side of the equation.(b) Factor the expression 8x2 + 27.(C) One of the factors of q? - bºis a - b. Find a quadratic factor of q? - bº. Show your work.(d) Factor the expression x - 1.
Given that the sum of two cubes can be factored by using the formula
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]a) To verify the formula by multiplying the right side equation
[tex]\begin{gathered} (a+b)(a^2-ab+b^2) \\ =a(a^2-ab+b^2)+b(a^2-ab+b^2) \\ =a^3-a^2b+ab^2+a^2b-ab^2+b^3 \\ \text{Collect like terms} \\ =a^3-a^2b+a^2b+ab^2-ab^2+b^3 \\ \text{Simplify} \\ =a^3+b^3 \end{gathered}[/tex]Hence,
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]b) To factor
[tex]8x^3+27[/tex]Using the sum of two cubes formula, i.e
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (2x)^3+(3)^3=(2x+3)((2x)^2-(2x)(3)+(3)^2)_{} \\ (2x)^3+(3)^3=(2x+3)(4x^2-6x+9) \end{gathered}[/tex]Hence, the answer is
[tex](2x+3)(4x^2-6x+9)[/tex]c) Given that one of the factors of a³ - b³ is a- b, the quadratic factor of a³ - b³ can be deduced by applying the differences of cubes formula below
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)^{}_{}[/tex]Expanding the right side equations
[tex]\begin{gathered} (a-b)(a^2+ab+b^2)^{}_{}=a(a^2+ab+b^2)-b(a^2+ab+b^2) \\ =a^3+a^2b+ab^2-a^2b-ab^2-b^3 \\ \text{Collect like terms} \\ =a^3+a^2b-a^2b+ab^2-ab^2-b^3 \\ \text{Simplify} \\ =a^3-b^3 \end{gathered}[/tex]Hence, the quadratic factor is
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]d) To factor the expression
[tex]x^3-1[/tex]By applying the differences of cubes formula
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (x)^3-(1)^3=(x-1)(x^2+(x)(1)+1^2)^{}_{} \\ x^3-1^3=(x-1)(x^2+x+1) \end{gathered}[/tex]Hence, the answer is
[tex](x-1)(x^2+x+1)[/tex]
4. Angelo gave 3 of a bag of pretzels to Ben. Ben ate a portion (x) of the pretzels and then gave 4 of the remaining pretzels in the bag to Connor. The expression below represents Connor's portion of the bag of pretzels. 2/3 314 Which expression is equivalent to Connor's portion of the bag of pretzels?
we have Connor's portion of the pretzels
[tex]\frac{2}{3}\times(\frac{3}{4}-x)[/tex]then simply the expression
[tex]\begin{gathered} \frac{2}{3}\times\frac{3}{4}-\frac{2}{3}x \\ \frac{2\times3}{3\times4}-\frac{2}{3}x \\ \frac{6}{12}-\frac{2}{3}x \\ \frac{1}{2}-\frac{2}{3}x \end{gathered}[/tex]answer: C
The portable basketball hoop shown is made so that BA = AS = AK. The measure of < BAK is 128 degrees. Calculate m < BSK.
The measure of ∠BSK is 64 degrees, that is the value of m∠BSK is 64 degrees.
We are given BA = AS = AK.
∠BAK = 128 degrees
From the linear pair concept:
∠BAK + ∠SAK = 180 degrees
128 degrees + ∠SAK = 180 degrees
∠SAK = 180 degrees - 128 degrees
∠SAK = 52 degrees
From the angle sum property of a triangle in triangle ASK, we will get;
∠SAK + ∠ASK + ∠AKS = 180 degrees
52 degrees + ∠ASK + ∠AKS = 180 degrees
2 ∠ASK = 180 degrees - 52 degrees (Since, AS = AK)
∠ASK = 128/2 degrees
∠ASK = 64 degrees
Thus, the measure of ∠BSK is 64 degrees, that is the value of m∠BSK is 64 degrees.
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Please help me solve question 6 on my algebra homework
We have the following equation:
[tex]y-5=2(x-2)[/tex]First, we leave the equation in the slope-intercept form.
[tex]\begin{gathered} y=2x-4+5 \\ y=2x+1 \end{gathered}[/tex]First, we leave the equation in the slope-intercept form.
Domain
The domain of a function is the set of the existence of itself, that is, the values for which the function is defined.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Range
The range of the function is the set of all the values that the function takes in the existing interval of the domain.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Zero
The zeros of a function are the points where the graph cuts the x-axis.
To find this, we equate the function to zero.
[tex]\begin{gathered} 2x+1=0 \\ x=-\frac{1}{2}=-0.5 \end{gathered}[/tex]In this case, the zero is in -0.5.
Y-intercept
To find the y-axis intercept, we solve the equation when x=0.
[tex]\begin{gathered} y=2\cdot0+1 \\ y=1 \end{gathered}[/tex]In conclusion, the y-axis intercept is in the coordinate (0,1)
Slope
Looking at the equation of the form y = mx+b we can easily tell what the slope is, remembering that "k" is the slope of the function.
[tex]\begin{gathered} y=2x+1 \\ k=2 \end{gathered}[/tex]In conclusion, the slope is k=2
Type of slope
There are four different types of slopes: negative, zero, positive and undefined.
In this case, the slope is positive, because the angle of the slope is greater than zero and less than 90 degrees.
In conclusion, the slope is positive
f(3)
We will solve the function when x=3
[tex]\begin{gathered} f(3)=2x+1 \\ f(3)=2\cdot3+1 \\ f(3)=6+1 \\ f(3)=7 \end{gathered}[/tex]Value of x, where f(x)=7
We must equal the function to 7 and clear "x".
[tex]\begin{gathered} 2x+1=7 \\ x=\frac{7-1}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]In conclusion, the value of "x" is x=3
I need help with geometry. I am supposed to solve for x in this diagram and assume lines marked with interior arrowheads are parallel :)
ANSWER:
40°
STEP-BY-STEP EXPLANATION:
We can make the following equality thanks to the properties of these angles:
[tex]\begin{gathered} 3x=120 \\ \text{ solving for x} \\ x=\frac{120}{3} \\ x=40\text{\degree} \end{gathered}[/tex]The value of x is 40°
Function A Function B Tell whether each function is linear or nonlinear. х y 4 0 1 3 5 24 8 2 3 13 0 1 2 3 4 5 Function A is a function. Function B is a function.
Function A is NOT LINEAR
Function B is LINEAR
The slope (change in y over change in x) does not follow a linear pattern in function A. That is the increase/decrease in the y coordinates is not at the same rate as that of the x coordinate. Whereas, for the other function, function B, the slope follows a linear pattern, that is the rate of change in y over the rate of change in x is the same rate, that is why function B has a straight line graph
brainstorm some real-world applications where integration could be helpful, then describe your examples and explain how integration fits in
Given
Integration
Find
some real-world applications where integration could be helpful
Explanation
In real life , integrations are used in vaarious fields such as engineering , where engineers use integrals to find the slope of the building
In physics , it is used in the centre of gravity .
In field of graphical representation , where three- dimensional models are demonstrated.
Final Answer
Hence , above are the some real world applications.
Summer earns 15% commission onsales for a software company. If inone week she makes three sales.one at $375, one at $1.200, and oneat $900. how much did Summerearn that week?
She made
[tex]375+1200+900=2475[/tex]in sales. Then, she earned
[tex]0.15(2475)=371.25[/tex]$371.25 that week.
7)Which table of values BEST represents a model of exponential decay?х012.34-12a(x)1a.251017-1012.34b.b(x)97531- 1х-101234cfx)346101834c.х-101234d.dx)191954723115
Answer:
the one that represents a model of experimental decay is d.
Step-by-step explanation:
In mathematics, exponential decay describes the process of REDUCING an amount by a consistent percentage rate over a period of time, it is different from linear decay because in linear decay factor relies on a percentage of the original amount, there is a constant rate of decay.
Therefore,
As we can see on the graphs, the only table of values that represent DECAYS is options b and d. But, notice option B is a linear decay since it has a constant rate of decay.
So, the one that represents a model of experimental decay is d.
write 37,000,010 numbers using words
thirty-seven million ten
Explanation
Step 1
count the number of digits after 37
[tex]\begin{gathered} 37000010 \\ 6\text{ digits, it meas} \\ by\text{ now, we have} \end{gathered}[/tex]thirty-seven million
Step 2
the remaining number is
[tex]\begin{gathered} 000010 \\ it\text{ is , ten} \\ 10 \end{gathered}[/tex]ten
Step 3
combine
thirty-seven million ten
4. Jill wants to buy $70,000 worth of insurance for her new house. If therate is $8.00 per $1000 of value, what will her insurance premium be?a. $590b. $560C. $530
Let's calculate the insurance premium Jill will have to pay for her insurance of her new home:
Insurance premium = 70,000 / 1,000 * 8
Insurance premium = 70 * 8
Now you can calculate easily the payment Jill will have to afford.
dominic is making meatballs. he uses 3/4 cup of breadcrumbs for every 1 1/4 pounds of ground beef. how many cups of bradecrumbs does he need when he uses 1 3/4 pounds of ground beef?
The number of cups of breadcrumbs he will need when he uses 3/4 pounds of ground beef would be = 1¹/20 cup.
What are breadcrumbs?Breadcrumbs is a type of food product that is produced from crumbling of dried bread which is used making dishes such as meatballs.
The number of cups of breadcrumbs for 1¼ of meat ball = ¾ cup
Therefore the number of cups of breadcrumbs for 1¾ = X cup.
That is ; 1¼ = ¾ cup
1¾ = X cup
Make X cup the subject of formula;
X cup = 1 ¾ × ¾ ÷ 1¼
X cup = 21/16 ÷ 5/4
X cup = 21/16 × 4/5
X cup = 21/20
X cup = 1 ¹/20 cup
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An equilateral triangle and an isosceles triangle share a common side. What is the measure of /_ABC?
The sum of all the angles in a triangle is equal to 180 degrees
For an equilateral triangle, all sides are equal
i.e 60 + 60 + 60= 180
For an isosceles triangle, two sides are equal
the first image is an isosceles triangle why the second image is an equilateral triangle
Complete the following tables 1 and 3 only.
Answer:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m
Explanation:
If two triangles are similar, their corresponding sides are proportional, so we can always use the following equation:
[tex]\frac{A}{B}=\frac{C}{D}[/tex]Therefore, for row (a), we can write the following equation:
[tex]\frac{5\frac{1}{2}}{1\frac{1}{4}}=\frac{2\frac{3}{4}}{D}[/tex]So, changing the mixed number by decimals and solving for D, we get:
[tex]\begin{gathered} \frac{5.5}{1.25}=\frac{2.75}{D} \\ 5.5D=2.75(1.25) \\ 5.5D=3.4375 \\ \frac{5.5D}{5.5}=\frac{3.4375}{5.5} \\ D=0.625 \end{gathered}[/tex]Then, for row (a), D = 0.625 = 5/8
In the same way, we can write and solve the following equation for row (b)
[tex]\begin{gathered} \frac{A}{23.4}=\frac{20.8}{15.6} \\ \frac{A}{23.4}\times23.4=\frac{20.8}{15.6}\times23.4 \\ A=31.2 \end{gathered}[/tex]For row (c), we get:
[tex]\begin{gathered} \frac{12}{B}=\frac{9}{6} \\ 12(6)=9(B) \\ 72=9B \\ \frac{72}{9}=\frac{9B}{9} \\ 8=B \end{gathered}[/tex]For row (d), we get:
[tex]\begin{gathered} \frac{4.5}{3.6}=\frac{C}{2.4} \\ \frac{4.5}{3.6}\times2.4=\frac{C}{2.4}\times2.4 \\ 3=C \end{gathered}[/tex]Therefore, the answers are:
(a) D = 5/8 in
(b) A = 31.2 cm
(c) B = 8 ft
(d) C = 3 m