y = 2/3x + 7 is slope-intercept form of the equation .
What exactly does slope intercept mean?
A method of expressing a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form.The point where the line is drawn the y-axis is known as the y-intercept, and the slope refers to how steep the line is.the equation of the parallel line in slope intercept form y=mx+b so that we can clearly see the slope and y intercept
2x-3y = -9
3y = 2x + 9
y = 2/3x + 9/3
y = 2/3x + 3
compare equation y = mx + c
slope = 2/3
to find c put x = -3 and y = 5
y = mx + c
5 = 2/3 * (-3) + c
5 = -6/3 + c
c = 5 + 2 = 7
put the final equation together
y = 2/3x + 7
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On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?
the length of the shadow is 30m
Explanation:hypotenuse = 50m
height of tree = 40 m
To solve the question, we will use an illustration:
To get the length of the shadow, we will apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = 50m, opposite = 40m
50² = 40² + shadow²
2500 = 1600 + shadow²
2500 - 1600 = shadow²
900 = shadow²
square root both sides:
[tex]\begin{gathered} \sqrt[]{900}\text{ = }\sqrt[]{shadow^2} \\ \text{shadow = 30 m} \end{gathered}[/tex]Hence, the length of the shadow is 30m
what is math all about.
Mathematics is a branch of science that deals with numbers, quantities and shapes. It includes arithmetic, geometric, algebra, calculus and many more. It also refers to the study of relationship between numbers or items.
One example is counting numbers which we are using almost everyday in our life.
1, 2, 3, 4 and so on.
275 x 56 using long multiplication
Answer:
15400
Step-by-step explanation:
Hope it helps and I hope you have a nice day!!! :)
BRAINIEST is appreciated it would really help!!!
When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.
If the next transaction on his statement shows
–
$30, which of these describes the transaction?
The next transaction statement can be described through option A) Thirty dollars was withdrawn if the next transaction on his statement shows –$30.
What is a Transaction statement?The term "Transaction Statement" refers to a statement that the lender may from time-to-time issue to any borrower, at the borrower's reasonable request or at the lender's option, listing the loans made, the inventory and accounts receivable they financed, as well as the terms and conditions of repayment.
A transaction can be said as a unit of work that is thus performed against a database. These transactions are units or mostly sequences of work that are accomplished in a logical order.
You can find your most recent statement via your bank branch because most banks allow you to generate statements through your online banking platform.
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Complete Question
When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.
If the next transaction on his statement shows –$30, which of these describes the transaction?
A) Thirty dollars was withdrawn
B) Money was neither deposited nor withdrawn
C) $30 was deposited
D) Seventy dollars was deposited
solve the equation for x
6x + 8 = 50
Answer:
x=7Step-by-step explanation:
To solve the equation for x, isolate it on one side of the equation.
6x+8=50Subtract by 8 from both sides.
6x+8-8=50-8
Solve.
50-8=42
6x=42
Divide by 6 from both sides.
6x/6=42/6
Solve.
Divide.
42/6=7
[tex]\Rightarrow \boxed{\sf{x=7}}[/tex]
Therefore, the solution is x=7, which is the correct answer.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6x + 8 = 50}[/tex]
[tex]\large\text{SUBTRACT \boxed{\textsf 8} to BOTH SIDES}[/tex]
[tex]\mathsf{6x + 8 - 8 = 50 - 8}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{8 - 8}} because it gives you 0}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{50 - 8}} because it help solve for the x-value}[/tex]
[tex]\mathsf{6x = 50 - 8}[/tex]
[tex]\large\text{New equation: } \mathsf{6x = 42}[/tex]
[tex]\large\text{DIVIDE \boxed{\mathsf{6}} to BOTH SIDES sides}[/tex]
[tex]\mathsf{\dfrac{6x}{6} = \dfrac{42}{6}}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{\dfrac{6}{6}}} because it gives you 1}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{\dfrac{42}{6}}} because it gives you the x-value}[/tex]
[tex]\mathsf{x = \dfrac{42}{6}}[/tex]
[tex]\mathsf{x = 7}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Need help with his practice problem, having troubleIt has an additional picture of a graph. Please help me with the graph, I will send a pic
Given the function:
[tex]f(x)=\sin (\frac{\pi x}{2})[/tex]To graph the function, we will identify the maximum and the minimum points
As we can see, the coefficient of the function = 1
So, the maximum will be at f = 1
And the minimum will be at f = -1
The period of the function will be as follows:
[tex]p=\frac{2\pi}{\frac{\pi}{2}}=4[/tex]So, beginning from the point (0, 0) then rise till we reach the maximum at ((1, 0) then complete the sine wave
The graph of the function will be as shown in the following picture:
jk has midpoint M(–17, 16.5) and endpoint K(–12, 4). What are the coordinates of endpoint J?
The coordinates of endpoint J which has the midpoint M(–17, 16.5) and endpoint K(–12, 4) is (-22,29)
Mid point:
Midpoint means the point that is in the middle of the line joining two points.
Given two points A (x)1, (y)1 and B (x)2, (y)2, the midpoint between A and B is given by,
M(x)3, (y)3 = [(x)1 + (x)2]/2, [(y)1 + (y)2]/2
where, M is the midpoint between A and B, and (x)3, (y)3 are its coordinates.
Given,
JK has midpoint M(–17, 16.5) and endpoint K(–12, 4).
Here we need to find the coordinates of endpoint J.
We know that formula of mid point through the given definition,
So let us consider
(x1, y1) = (a, b)
(x2, y2) = (-12,4)
Now we have to apply the values on the formula in order to solve it,
Therefore,
(-17, 16.5) = (a + (-12))/2 , (b + 4)/2
Compare the values individually, then we get,
-17 = (a - 12) / 2
-17 x 2 = a - 12
- 34 = a - 12
a = -34 + 12
a = -22
Similarly, when we take the second part,
16.5 = (b+4)/2
16.5 x 2 = b + 4
33 = b+ 4
b = 33 - 4
b = 29
Therefore, the coordinate end points of J is (-22, 29).
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l need help with this please
Answer:
Step-by-step explanation:
y = 4 - 2x
8/11 when rounded is closer to 1 than 0? True False
Answer: False?
Step-by-step explanation:
Answer:
It is closer to [tex]1[/tex] than [tex]0[/tex], so the statement is True.
Step-by-step explanation:
Step 1: Finding the decimal form of [tex]\frac{8}{11}[/tex]
Upon simplification on a calculator, we can see that the exact value of [tex]\frac{8}{11}[/tex] is:
[tex]0.7272727273[/tex]
Let's round this to [tex]0.73[/tex] for an easier time.
Step 2: Identifying the value's difference from 1 and 0
We have found the value of the fraction to be [tex]0.73[/tex].
If we subtract the value from [tex]1[/tex], we get:
[tex]1-0.73\\=0.27[/tex]
If we find the difference between it and [tex]0[/tex], we get:
[tex]0.73-0\\=0.73[/tex]
As we can see, the value is [tex]0.27[/tex] units away from [tex]1[/tex], but is [tex]0.73[/tex] units away from [tex]0[/tex].
We can clearly see that it is closer to [tex]1[/tex], so the statement is True.
Calculate the variance and standard deviation ofthe samples, using the appropriate symbols to label each
To determine the variance of a sample we can use the following formula:
[tex]s^2=\frac{\sum(x_i-\bar{x})}{n-1},[/tex]where
[tex]\bar{x}\text{ }[/tex]is the mean of the dataset.
The standard deviation is the square root of the variance.
Recall that the mean of a dataset is the sum of the number divided by the number of numbers, therefore, the mean of the given dataset is:
[tex]\bar{x\text{ }}=\frac{50.0+51.5+53.0+53.5+54.0}{5}=52.4.[/tex]Substituting the above result in the formula for the variance, we get:
[tex]s^2=2.675.[/tex]Therefore, the standard deviation is:
[tex]s=1.6355427.[/tex]Answer:
Variance:
[tex]s^2=2.675.[/tex]Standard deviation:
[tex]s=1.6355427.[/tex]I couldn’t fit all the answers on the screen but the fourth option is all positive numbers
Answer:
Alternative C - All real numbers.
Step-by-step explanation:
The domain of an function is the set of all possible numbers which x can assume.
As we can see, we have no restrictions for x.
So, the domain is all real numbers.
Answer: Alternative C - all real numbers.
(d) Find the domain of function R. Choose the correct domain below.
Answer:
last answer is right
( but x can be any number not just x>=0 )
need help with this problem Its not the first one
Solution:
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints and contains every point on the line that is between its endpoints. The angle of rotational symmetry or angle of rotation is the smallest angle for which the figure can be rotated to coincide with itself.
A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation
Rotation of a line does not change the length of the line segments
Reflection does not preserve orientation.
Dilation (scaling), rotation, and translation (shift) do preserve it.
Hence,
The final answer is the THIRD OPTION
A certain television is advertised as a 5-inch TV. If the width of the TV is 4 inches, how many inches tall is the TV
Answer:
The TV is 3 inches tall.
[tex]3\text{ inches}[/tex]Explanation:
Given that the width of the TV is
[tex]4\text{ inches}[/tex]And the TV is 5 inch TV, which means its diagonal is;
[tex]d=5\text{ inches}[/tex]The height of the TV can be calculated using the Pythagoras Theorem;
[tex]\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]substituting the diagonal and the width;
[tex]\begin{gathered} b=\sqrt[]{5^2-4^2} \\ b=\sqrt[]{25-16} \\ b=\sqrt[]{9} \\ b=3\text{ inches} \end{gathered}[/tex]Therefore, the TV is 3 inches tall.
[tex]3\text{ inches}[/tex]four inches of a (somewhat magnified ) ruler is shown. use the ruler to give the length of the gray bar, to the nearest sixteenth of an in. write answer as a mixed #. (simplify as much as possible)
We have the following:
We have that 4 is equal to 64/16
[tex]\frac{4\cdot16}{1\cdot16}=\frac{64}{16}[/tex]Thefore:
The bar is found in 2 and 15 more lines, each line is 1/16
[tex]\frac{2\cdot16}{1\cdot16}+\frac{15}{16}=\frac{32}{16}+\frac{15}{16}=\frac{47}{16}=2\frac{15}{16}[/tex]Can you please show me how to check the answer to see if it is right.
We are given the equation;
[tex]-7=\sqrt[3]{9x-1}-3[/tex]Collect like terms
[tex]\begin{gathered} -4=\sqrt[3]{9x-1} \\ (-4)^3=(\sqrt[3]{9x-1})^3 \\ -64=9x-1 \\ -63=9x \\ x=-7 \end{gathered}[/tex]To check this, we insert the x value into the original equation, if it gives both sides equal, it is correct.
[tex]\begin{gathered} -7=\sqrt[3]{9x-1}-3 \\ -7=\sqrt[3]{9(-7)-1}-3 \\ -7=\sqrt[3]{-64}-3 \\ -7=-4-3 \\ -7=-7 \end{gathered}[/tex]Therefore, the answer is -7
to put it in graphing form and then graphY=x^2-6x+3
We have the following:
[tex]\begin{gathered} y=x^2-6x+3 \\ f(x)=x^2-6x+3 \end{gathered}[/tex]now, we must give values to x, to be able to graph
[tex]\begin{gathered} f(-2)=x^2-6x+3=(-2)^2-6\cdot-2+3=19 \\ f(-1)=x^2-6x+3=(-1)^2-6\cdot-1+3=10 \\ f(0)=x^2-6x+3=(0)^2-6\cdot0+3=3 \\ f(1)=x^2-6x+3=(1)^2-6\cdot1+3=-2 \\ f(2)=x^2-6x+3=(2)^2-6\cdot2+3=-5 \end{gathered}[/tex]The grahp is:
Find m
Which answer is correct
The value of angle EFG is 50°.
What is angle?An angle results from the intersection of two straight lines or rays at a single terminal.
Angles' Components
Vertex: The intersection of two lines or sides at an angle is called a vertex.
Arms: The angle's two sides linked at a single end.
Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line.
∵ exterior angle = sum of opposite interior angles
∴ 7x+18 = (6x-10) + 38
7x + 18 = 6x +28
x = 10°
∴∠EFG = 6*10-10
∠EFG = 50°
Option (B) is correct answer.
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For triangle ABC, a = 7.7 , b = 17.0 , c = 12.7. Find m∠C.
The triangle can be drawn as shown below:
The Cosine Rule can be applied in this case. It is given to be:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ \cos C=\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]From the question, we have the following measures:
[tex]\begin{gathered} a=7.7 \\ b=17.0 \\ c=12.7 \end{gathered}[/tex]Therefore, we can substitute and solve as shown below:
[tex]\begin{gathered} \cos C=\frac{7.7^2+17.0^2-12.7^2}{2\times7.7\times17.0} \\ \cos C=\frac{187}{261.8} \\ \cos C=0.714 \end{gathered}[/tex]Therefore, the measure of angle C will be gotten to be:
[tex]\begin{gathered} C=\cos ^{-1}0.714 \\ m\angle C=44.4\degree \end{gathered}[/tex]The measure of angle C is 44.4°.
Which is the solution to the equation: 0.435 + x = 0.92*x = 1.355O x= 0.595x = 0.4950 x = 0.485Send me a copy of my responses.
To answer this question, we need to subtract 0.435 to both sides of the equation as follows:
[tex]0.435-0.435+x=0.92-0.435\Rightarrow x=0.485_{}[/tex]Therefore, the solution for x in this equation is x = 0.485 (last option).
Solve the following problem. Give the equation using x as the variable, and give the answer.If 4 is added to five times a number, the result is equal to 7 more than four times the number. Find thenumber.Write the equation using x as the variable. Choose the correct equation below.O A. 4(5x) = 7(4x)O B. 5(x + 4) = 4(x + 7)O C. 5x + 4 = 7(4x)OD. 5x + 4 = 4x + 7O E. 4(5x) = 4x + 7The number is
Answer
[tex]\begin{gathered} D. \\ 5x+4=4x+7 \\ \text{The number is 3} \end{gathered}[/tex]Explanation
The variable given is x
Five times the variable is 5x
When 4 is added, the expression becomes 5x + 4, which gives the Left Hand Side of the equation.
For the Right Hand Side, four times the number is 4x
7 more than 4x is 4x + 7
Since the result on the Left Hand Side = Right Hand Side, then the required equation is
[tex]5x+4=4x+7[/tex]Now, to find the number x, we shall solve the above equation as follows
[tex]\begin{gathered} 5x+4=4x+7 \\ \text{Substract 4 from both sides} \\ 5x+4-4=4x+7-4 \\ 5x=4x+3 \\ \text{Substract 4x from both sides} \\ 5x-4x=4x+3-4x \\ x=3 \end{gathered}[/tex]What is the slope-intercept form(-2,-1),(-4,-3)
To solve the exercise, we can first find the slope of the line that passes through the given points using the following formula:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} (x_1,y_1)=(-2,-1) \\ (x_2,y_2)=(-4,-3) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-3-(-1)}{-4-(-2)} \\ m=\frac{-3+1}{-4+2} \\ m=\frac{-2}{-2} \\ m=1 \end{gathered}[/tex]Now, we can use the point-slope formula, and we solve for y:
[tex]y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula}[/tex][tex]\begin{gathered} y-(-1)=1(x-(-2)) \\ y+1=x+2 \\ \text{ Subtract 1 from both sides of the equation} \\ y+1-1=x+2-1 \\ y=x+1 \end{gathered}[/tex]Therefore, the equation of the line that passes through the points (-2, -1) and (-4, -3) in its slope-intercept form is:
[tex]$$\boldsymbol{y=x+1}$$[/tex]Elijah earned a score of 64 on Exam A that had a mean of 100 and a standarddeviation of 20. He is about to take Exam B that has a mean of 600 and a standarddeviation of 40. How well must Elijah score on Exam B in order to do equivalentlywell as he did on Exam A? Assume that scores on each exam are normally distributed.
Notation:
μ = mean
σ = standard deviation
Exam A:
[tex]\begin{gathered} \mu=100 \\ \sigma=20 \end{gathered}[/tex]The score of the exam is 64, so we calculate the z-score given that scores on the exam are normally distributed. The formula of the z-score is:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Now, for X = 64:
[tex]Z=\frac{64-100}{20}=-1.8[/tex]Exam B:
[tex]\begin{gathered} \mu=600 \\ \sigma=40 \end{gathered}[/tex]Now, we need to find a z-score equal to that of the score on Exam A. This z-score is -1.8, and the score on exam B should be:
[tex]\begin{gathered} -1.8=\frac{X-600}{40} \\ -72=X-600 \\ \therefore X=528 \end{gathered}[/tex]The score on exam B should be 528 in order to do equivalently well as he did on Exam A
Find the length of the third side. If necessary, round to the nearest tenth.914
The given trinagle is a right angle triangle. let the missing side be x. To find x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the triangle,
hypotenuse = 14
one leg = 9
other leg = x
Thus, we have
[tex]\begin{gathered} 14^2=9^2+x^2 \\ 196=81+x^2 \\ x^2\text{ = 196 - 81 = 115} \\ x\text{ = }\sqrt[]{115} \\ x\text{ = 10.72} \end{gathered}[/tex]To the nearest tenth, the length of the third side is 10.7
I just need to know what do I do when it says 2t but t is 10.M - t squared 2 / (M+p) + 2t
Solution:
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]m-t^2\div(m+p)+2t[/tex]STEP 2: Write the given values
[tex]t=10,m=3,p=2[/tex]STEP 3: Substitute the values and simplify
[tex]\begin{gathered} 3-(10^2)\div(3+2)+2(10) \\ Follow\:the\:PEMDAS\:order\:of\:operations \end{gathered}[/tex]We solve the bracket first:
[tex]=3-100\div5+20[/tex]We solve the division operator next:
[tex]\begin{gathered} 3-(100\div5)+20 \\ 3-20+20 \end{gathered}[/tex]We do the addition and subtraction simultaneously to have:
[tex]3+0=3[/tex]Hence, the result of the simplification gives 3
Suppose you invest $5,000 at 4% annual interest. How much money would your investment be worth after 10 years? Round your answer to the nearest hundredth (2 places after the decimal).
The investment will be worth $7,401.22 after 10 years
Here, we want to calculate the amount the investment will be worth after 10 years
Mathematically, to get this, we will use the compound interest formula;
[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where A is the amount after 10 years
P is the amount invested which is $5,000
r is the interest rate which is 4%, same as 4/100 = 0.04
n is the number of terms yearly the investment will be compounded. Since the interest rate is annual, then the number of times it will be compounded yearly is 1
t is the number of years which is 10 in this case
Substituting these values, we have;
[tex]\begin{gathered} A\text{ =5000 (1 + }\frac{0.04}{1})^{1\times10} \\ \\ A=5000(1+0.04)^{10} \\ \\ A=5000(1.04)^{10} \\ \\ A\text{ = 7,401.22} \end{gathered}[/tex](d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative. This eliminates all of the options except for d.
“K+273 gives the temperature in kelvins(K) for a given temperature in degrees Celsius.What is the temperature in kelvins when the temperature is 55 degrees Celsius?” Evaluate the expression
we have that
The temperature T in degrees Celsius (°C) is equal to the temperature T in Kelvin (K) minus 273.15
so
°C=K-273.15
For T=55°C
substitute
55=k-273.15
solve for k
k=55+273.15
K=328.15°standard form and contain only positive exponents 21c^10d^3+56c^6d^2-7c^2d------------------------------------------- 7c^2d
To solve this problem it is necessary to simplify the expression.
Step 1. Write the equation as a sum of homogeneous fractions:
[tex]\frac{21c^{10}d^3+56c^6d^2-7c^2d}{7c^2d}=\frac{21c^{10}d^3}{7c^2d}+\frac{56c^6d^2}{7c^2d}-\frac{7c^2d}{7c^2d}[/tex]Step 2. Simplify the obtained expressions:
[tex]\begin{gathered} \frac{21c^{10}d^3}{7c^2d}=3c^8d^2 \\ \frac{56c^6d^2}{7c^2d}=8c^4d \\ \frac{7c^2d}{7c^2d}=1 \end{gathered}[/tex]Step 3. Rewrite the expression using the simplified terms:
[tex]3c^8d^2+8c^4d-1[/tex]If you would like to make $1323 in 7 years, how much would you have to deposit in an account that pays simple interest of 2%?
A = $13,366.37
A = P + I where
P (principal) = $10,000.00
I (interest) = $3,366.37