Write the equation of the line in slope intercept form that passes through the points (-1,1) and (2,13)
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, 1) and (2, 13). Substitute:
[tex]m=\dfrac{13-1}{2-(-1)}=\dfrac{12}{3}=4[/tex]
Therefore the equation of a line is
[tex]y=4x+b[/tex]
Put the coordinates of the point (2, 13) to the equation of a line:
[tex]13=4(2)+b[/tex]
[tex]13=8+b[/tex] subtract 8 from both sides
[tex]5=b\to b=5[/tex]
Answer: y = 4x + 5What is 2/5 - [-4 7/10]
Answer: 5 1/10
Solution:
2/5-[-4 7/10]
2/5-[-(4*10+7)/10]
2/5-[-(40+7)/10]
2/5-[-47/10]
2/5+47/10
2*2/(5*2)+47/10
4/10+47/10
(4+47)/10
51/10
(50+1)/10
50/10+1/10
5 1/10
Twenty-seven is the product of three and a number
It’s the product of three and nine.
help my on these two questions plss
7. Loan amount = $12000
Monthly payment = $380
Duration of the repayment = 3 years = 3(12) = 36 months.
Total amount Jason repaid = 36 × 380 = 13680
Interest on loan amount = amount repaid - loan amount
= 13680 - 12000
= 1680
Hence, total amount Jason paid in interest on loan = $1680 and the correct option is (D).
8. Loan amount = $35000
Monthly payment = $315
Duration of the repayment = 10 years = 10(12) = 120 months.
Total amount Gerald repaid = 120 × 315 = 37800
Interest on loan amount = amount repaid - loan amount
= 37800 - 35000
= 2800
Hence, total amount Gerald paid in interest on loan = $2800 and the correct option is (B).
3 more than a number t is greater than or equal to 21
The equation is saying [tex]t+3\geq 21[/tex]. We can use algebra to subtract 3 from both sides to create [tex]t\geq 18[/tex].
Therefore, the value t is greater or equal to 18.
estimate 771 divided by 3.6
Final answer:
To estimate the division of 771 by 3.6, round 3.6 to 4 and divide 771 by 4 to get an approximate result of 192.75.
Explanation:
To estimate 771 divided by 3.6, we can round 3.6 to the nearest whole number, which is 4. The estimation calculation would then be 771 ÷ 4. Dividing 771 by 4 can be done by breaking down 771 into 760 + 11. Now, 760 ÷ 4 equals 190, and 11 ÷ 4 is approximately 2.75. Adding these two results, we get an estimated total of 192.75. Therefore, the estimated result of 771 ÷ 3.6 is approximately 192.75.
A dolphin traveled 5 miles in 15 minutes, a stingray traveled 11 miles in 30 minutes, and a great white shark traveled 92 miles in 4 hours. Which animal Is the fastest?
Dolphin: 5/15=1/3= .3333- miles per minute
Stingray: 11/30= .3666- miles per minute
Great White Shark: 92/(4 x 60)= .38333- miles per minute
The great white shark is the fastest.
Answer:
The great white shark is the fastest.
Step-by-step explanation:
HELP ASAP!!!!!!!!!!!!!!
What is an equation of the line that is parallel to y=3x−8 and passes through (1, 8) ?
Im pretty sure its y = 3x - 17
put the following decimals in order from least to greatest 4.08; 4.3; 4.803; 4.038
Answer:
4.038 < 4.08 < 4.3 < 4.803
Step-by-step explanation:
We are given four decimal numbers and we have to arrange them in increasing order:
The numbers are 4.08, 4.3, 4.803, 4.038
The expanded form of these decimal numbers are:
[tex]4.08 = 4 + \displaystyle\frac{8}{100}[/tex]
[tex]4.3 = 4 + \displaystyle\frac{3}{10}[/tex]
[tex]4.803 = 4 + \displaystyle\frac{8}{10} + \displaystyle\frac{3}{1000}[/tex]
[tex]4.038 = 4 + \displaystyle\frac{3}{100} + \displaystyle\frac{8}{1000}[/tex]
Thus, the increasing order is:
4.038 < 4.08 < 4.3 < 4.803
Select from the drop down menus to correctly complete each statement. - 15 < -13 - 13 < - 11 is - 13 located to the right or to the left of -15 on the number line. is - 11 located to the left or the right of - 13 on a number line.
On the number line, smaller numbers are located to the left of larger numbers, which are located on the right.
So, if you have two numbers x and y on the number line, the smaller of the two will be on the left, the larger one on the right.
So, -13 is located to the right of -15, because it's larger.
For the same reason, -11 is located to the right of -13.
On the number line, you would have something like
<--------(-15)-------(-13)--------(-11)---------->
On a number line, negative values decreases as we move to the left while positive values increases to the right. Hence,
-13 is located to the right of - 15 -11 is located to the right of - 13Starting from 0 to the left, we have - 1, - 2, - 3,... which continues in that sequence as decreases as we move to the left of the number line.
Moving towards the left, - 13 appears before - 15 ; Hence - 13 is located relative to the right of - 15 on the number line
Similary, - 11 appears before - 13 ; Hence - 11 is located relative to the right of - 13 on the number line.
Therefore, - 13 and - 11 are located to the right of - 15 and - 13 respectively on the number line.
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Simplify the following expression.
12 - 5[(4 + 2)/\2 - (22 + 10)]
A.
-198
B.
-238
C.
-18
D.
-98
12 - 5[(4 +2)² - (22 + 10)]
Remember to follow PEMDAS. First, solve both parenthesis
12 - 5[(4 +2)² - (22 + 10)]
12 - 5[(6)² - (32)]
Next, solve the exponent
(6)² = 6 x 6 = 36
12 - 5[(36) - (32)]
Then, solve the bracket.
36 - 32 = 4
12 - 5[4]
Next, multiply
-5 x 4 = -20
Finally, subtract.
12 - 20 = -8
None of the above. The answer is -8. Please check the answers and the question again
~Rise Above the Ordinary
a 21-ounce box of cereal costs $2.94, what is the unit price? what is the unit price?
I'm pretty sure the unit price is $0.14. :)
Keisha solved the following equation: 4x − 2x + 8 = 6(x + 4) Step Work Justification 1 2x + 8 = 6(x + 4) Combine like terms 2 2x + 8 = 6x + 24 Associative property of multiplication 3 −4x + 8 = 24 Subtraction property of equality 4 −4x = 16 Addition property of equality 5 x = −4 Division property of equality
4x - 2x + 8 = 6(x + 4) Given
(4x - 2x) + 8 = 6(x + 4)
2x + 8 = 6(x + 4) Combine like terms
2x + 8 = (6)(x) + (6)(4)
2x + 8 = 6x + 24 Distributive Property
2x - 6x + 8 = 6x - 6x + 24
-4x + 8 = 24 Subtraction Property of Equality
-4x + 8 - 8 = 24 - 8
-4x = 16 Subtraction Property of Equality
-4x : (-4) = 16 : (-4)
x = -4 Division Property of Equality
Compare 2.3 and 2.03
what is the value of (x+3) folders at $0.10 each
7+3 =10 or 3(10) 30
Rachel earns $21 per day for 22a-22d select true or false for each statement
22a. False
22b. True
22c. True
22d. False
For each scenario, we multiply Rachel's daily earnings ($21) by the number of days worked to find her total earnings.
In 22a, Rachel earns 21 × 20 = $420, not $421 as stated.
In 22b, Rachel indeed earns 21 × 15 = $315, making the statement true.
Similarly, in 22c, Rachel earns 21 × 13 = $273, confirming the statement as true.
However, in 22d, Rachel's earnings for 13 days amount to 21 × 13 = $273, not $250, rendering the statement false.
Therefore, the true statements are 22b and 22c, while 22a and 22d are false.
Complete Question:
2 times 5 times 10 to the 5th power
2x5x10^5=1000000. You do the exponent first,10^5 = 100000. Then you multiply that by 5, 5x100000=500000. Then by 2, 500,000x2= 1000000.
spencer hits a tennis ball past his opponent. the height of the tennis ball in feet is modeled by the equation h(t)=-0.075t^2+0.6x+2.5 where t is the time since the tennis ball was hit meausured in seconds. how long does it take for the ball to reach its maximum height?
The quadratic function is given by the equation [tex]h(t)=-0.075t^2+0.6t+2.5.[/tex]
The maximal height will be at vertex. Find t-coordinate of the parabola vertex:
[tex]t_{vertex}=-\dfrac{b}{2a}=-\dfrac{0.6}{2\cdot (-0.075)}=4\text{ seconds.}[/tex]
At t=4,
[tex]h(4)=-0.075\cdot 4^2+0.6\cdot 4+2.5=-1.2+2.4+2.5=3.7\text { feet. }[/tex]
Answer: it will take 4 seconds for the ball to reach the maximal height of 3.7 feet.
A function follows the rule y = -75 - 5 x . When the function's output is 25, the equation is 25 = -75 - 5 x . What is the function input when the output is 25? 20 -20 10 -10
Answer: C. -20
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what is the place value of the 8 in 2,894?
The place value of the 8 in 2,894 would be the hundredths.
Hope helps!-Aparri
the value of the eight is 800 because i actually dont know how to explain this but basiclly the 3 rd digit from the right would always be the hundereds place.
Which operation is NOT closed for polynomials?
A) add a trinomial to a trinomial
B) divide a binomial by a trinomial
C) multiply a binomial by a binomial
D) subtract a binomial from a trinomial
Answer:
Option B is the correct choice.
Step-by-step explanation:
Since we know that polynomials are closed under addition, subtraction and multiplication but not under division because division of two polynomials is not necessarily a polynomial.
Dividing a binomial by a trinomial will result in a rational expression and it will have negative exponent. Negative exponents are not allowed in polynomials.
Therefore, option B is the correct choice.
how many planes can two distinct lines have in common
either 0 or 1 plane(s)
A certain triangle has 30 angle and 60 angle which much be a true statement about the triangle
Answer:
D
Step-by-step explanation:
The longest side is twice as long as the shortest side because lets suppose I have a triangle that has vertices with angles 30 and 60, the last one has to be 90 because the total is 180 degrees. Now for a 30 60 triangle, if the hypotenuse has a length of 2, the following ratios will hold true for the other two sides. The side that shares the 90 degrees and 60 degrees corners will be of length 1 and the side that shares the 30 degrees and 90 degrees corners (vertices) will be of length sqrt(3). This is true all the time. In this case the correct answer is that the longest side is twice as long as the shortest side because the longest side is the hypotenuse with length 2 and the shortest side will be the one that shares the 90 degrees and 60 degrees corners and is of length 1.
Answer:
A
Step-by-step explanation:
How would u do -6-(-1)=
The answer would be -5 because:
-6-(-1)
Keep Change Flip
-6 + 1
Different signs Subtract..so the answer would be 5 but then you add the negative to it because -6 is greater than the positive 1
Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(x+6)feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?
SHOW ALL WORK
Given dimensions of a rectangular garden are:
length = 2(x+6) feet
width = 3.5x feet
using the distributive property on length we get, length = 2x+12
Perimeter of a rectangle is 2(length+width)
So, P = 2(2x+12+3.5x)
Solving it we get,
P = 2(5.5x +12) ..............adding like terms
P = [tex](2\times5.5)+(2\times12)[/tex] .............multiplying and adding
P = 11x+24
So, perimeter is 11x+24 feet. This value of fencing will be needed.
Would you consider these shapes congruent??
no it would not be congruent
Hello!
Answer:No, these shapes would not be considered congruent. In geometry, figures would only be congruent if they have the same size and shape. In the above image, the two figures have the same shapes, but they do not have the same size.
The variable, usually on the x-axis, which is used to predict y-values, is called the ____ variable. It is also sometimes called the explanatory variable.
Answer: Independent variable
Step-by-step explanation:
The variable usually on the x-axis, which is used to predict y-values, is called the Independent variable.
Discussion:
In most mathematical relations including linear programming problems; we usually have a combination of two variables namely;
Dependent andIndependent variableThe variable whose value determines the value of other variables is termed the independent variable and is usually plotted on the x-axis.
Read more on independent variable:
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I need this today ASAP!!!!
-4 1/2 + 1/3
The answer of this expression is - 4 1/6
simplify the following expression into the form a+bi where a and b are rational numbers
(3+7i) (-2-2i) -4i(5-9i)
Answer:
- 28 - 40i
note that i² = (√-1)² = - 1
expand product of factors using FOIL
= - 6 - 6i - 14i - 14i² - 20i + 36i²
= - 6 - 6i - 14i + 14 - 20i - 36
= - 28 - 40i
Step-by-step explanation:
Got right on PLATO
The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i
What is a complex number?A complex number is a number of the form a + bi, where a and b are real numbers, and i = √-1
i² = (√-1)² = -1
Given the expression:
(3+7i) (-2-2i) -4i(5-9i)
= -6 - 14i -6i + 14 - 4i(5 - 9i)
= 8 - 20i - 20i - 36
= -28 - 40i
The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i
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I dont understand this please help me
A.) 34.68
hope this helps
A is your answer. Take the $289 and multiply that by 0.12.
Hope this helps & good luck. :)