The equation 5x − 14y = 16, when rewritten in slope-intercept form, is[tex]y = (5/14)x - 8/7.[/tex]
Explanation:To rewrite the given equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we'll isolate y. Starting with the equation 5x − 14y = 16:
1. Subtract 5x from both sides to move the x term to the other side:
-14y = -5x + 16
2. Divide every term by -14 to solve for y:
y = (5/14)x - 8/7
In this form, the coefficient of x represents the slope (m), which is 5/14, and the constant term is the y-intercept (b), which is -8/7. The slope indicates the rate of change of y concerning x, and the y-intercept represents the point where the line intersects the y-axis.
By following these steps, we've successfully transformed the given equation into slope-intercept form, making it easier to interpret and work within the context of linear relationships.
To convert the equation 5x - 14y = 16 to slope-intercept form, solve for y to yield y = (5/14)x - 8/7, where the slope is 5/14 and the y-intercept is -8/7.
Explanation:To rewrite the equation 5x − 14y = 16 in slope-intercept form, we need to solve for y to get the equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
First, we subtract 5x from both sides of the equation:5x − 14y − 5x = 16 − 5xThis simplifies to −14y = −5x + 16.Next, we divide each term by −14 to solve for y:y = (−5x + 16) / −14Finally, we simplify the equation:y = (5/14)x − 16/14In simplified form, the slope-intercept form of the equation is y = (5/14)x − 8/7. Here, the slope (m) is 5/14 and the y-intercept (b) is −8/7.
the length of a rectangular garden is 4 m greater than the width. the area is 96 m to the second. find the dimensions of the garden.
A dripping faucet leaks 12 gallons of water per day. How many gallons does the faucet leak in 6 days?
An iron bar 468 3/4 inches long is to be cut into 6 1/4 inch sections. How many sections of this length will there be?
Luis skates 2/3 mile from his home to school. Isabella skates 2/4 mile to get to school. Who skates father?
Final answer:
Luis skates further to school than Isabella, as 2/3 mile is greater than Isabella's distance of 1/2 mile after simplification.
Explanation:
The question revolves around figuring out who skates further to school, Luis or Isabella. Luis skates 2/3 mile from his home to school whereas Isabella skates 2/4 mile (which can be simplified to 1/2 mile) to get to school. To determine who skates further, we look at the fraction representing the distance each person skates.
Luis's distance is 2/3 mile, and Isabella's distance, after simplification, is 1/2 mile. Since 2/3 is greater than 1/2, Luis skates further to get to school than Isabella.
What is the approximate solution of this system of equations?
y = x2 + 3x + 3
y = x2 + x + 2
(-0.5, 0.2)
(-0.5, 1.7)
(-0.1, 1.2)
(0.2, 1.5)
Answer:
(B)
Step-by-step explanation:
The given system of equations are:
[tex]y=x^2+3x+3[/tex] (1)
and [tex]y=x^2+x+2[/tex] (2)
Subtracting equation (2) from (1), we get
[tex]0=2x+1[/tex]
⇒[tex]2x=-1[/tex]
⇒[tex]x={\frac{-1}{2}}[/tex]
⇒[tex]x=-0.5[/tex]
Now, substituting the value of x=-0.5 in equation (2), we get
[tex]y=0.25-0.5+2[/tex]
⇒[tex]y=1.7[/tex]
Thus, the values of x and y are -0.5 and 1.7.
Therefore, the approximate solution of the given system of the equation is (-0.5, 1.7).
Hence, option (B) is correct.
What is the value of x in simplest radical form ?
Help from 1-3 show work please!!
Putri is searching for a secret cave that she knows is 3.72 kilometers from her home. Starting from her home, she walks 2.60 kilometers in a straight line before coming upon a large rock.
Climbing atop the rock, Putri spots the cave. She then turns 58 degrees to the right of her original path and walks to the cave. After exploring the cave, she looks back at the big rock and wonders how to get home.
Assuming Putri is facing the big rock, how many degrees to her left should she turn before walking home?
The Putri turned 36 degrees to her left should she turn before walking home if Putri is searching for a secret cave that she knows is 3.72 kilometers from her home. Starting from her home, she walks 2.60 kilometers in a straight line before coming upon a large rock.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have:
The total distance between cave to home AC = 3.72 km
The distance she walks AB = 2.60 km
The angle of turn = 58°
As we can see in the triangle ABC we can apply the sin law:
[tex]\rm \frac{AB}{sinx} = \frac{AC}{sin58\°}[/tex]
[tex]\rm \frac{2.6}{sinx} = \frac{3.72}{sin58\°}[/tex]
sinx = 0.5927
x = 36.35 ≈ 36°
Thus, the Putri turned 36 degrees to her left should she turn before walking home if Putri is searching for a secret cave that she knows is 3.72 kilometers from her home. Starting from her home, she walks 2.60 kilometers in a straight line before coming upon a large rock.
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Putri should turn 122 degrees to her left when facing the big rock to head back to her home. This direction aligns her with the original path she took to reach the cave.
To determine the number of degrees to her left Putri should turn, we need to analyze her movements using the angles involved.
Putri starts by walking 2.60 kilometers in a straight line.She spots the cave after climbing the rock and turns 58 degrees to the right of her original path.This new path takes her directly to the cave, which is a straight-line distance of 3.72 kilometers from her home.When Putri is in the cave facing the large rock, to get back to her home, she needs to turn in the opposite direction of her initial right turn:
Initially, she turned 58 degrees to the right.Facing the rock, she must turn 180 degrees - 58 degrees = 122 degrees to her left to be aligned with her starting path towards home.Putri should turn 122 degrees to her left when facing the big rock to head back to her home.
This week Luis made 80% of what he made last week. If he made $72 this week, how much did he make last week
estimate the area of a circle with a radius of 27 meters
How does the graph of g(x)=⌈x⌉+0.5 differ from the graph of f(x)=⌈x⌉?
A. The graph of g(x)=⌈x⌉+0.5 is the graph of f(x)=⌈x⌉ shifted up 0.5 unit.
B. The graph of g(x)=⌈x⌉+0.5 is the graph of f(x)=⌈x⌉ shifted left 0.5 unit.
C. The graph of g(x)=⌈x⌉+0.5 is the graph of f(x)=⌈x⌉ shifted down 0.5 unit.
D. The graph of g(x)=⌈x⌉+0.5 is the graph of f(x)=⌈x⌉ shifted right 0.5 unit.
Answer: Here is your answer!! :)
Step-by-step explanation:
If 16-7w=w+14-6w16−7w=w+14−6w16, minus, 7, w, equals, w, plus, 14, minus, 6, w, what is the value of w-1w−1w, minus, 1?
Answer:
Value of w = 1
w - 1 = 1 - 1 = 0
Explanation:
We have 16 - 7w = w + 14 - 6w
Firstly, we will find the value of w.
In order to find the value of w, we will solve the linear equation for w.
Now combine like terms
16 - 14 = w - 6w + 7w
2 = 2w
2w = 2
w = [tex] \frac{2}{2} [/tex]
w = 1
Now we will find the value of w - 1
Plug the value of w = 1 into w - 1
1 - 1
= 0
So, final answer is 0
I hope it will help you.
Dominic is building a bench with a seat in the shape of a trapezoid. One base is 5 feet. The other base is 4 feet. The perpendicular distance between the bases is 2.5 feet. what is the area of the seat
The area of Dominic's trapezoid-shaped bench seat is 11.25 square feet. This is calculated using the trapezoid area formula with given bases of 5 and 4 feet and a height of 2.5 feet.
To find the area of the seat of Dominic's bench, which is in the shape of a trapezoid, we use the formula for the area of a trapezoid:
Area = 1/2 × (Base1 + Base2) × Height
In this case:
Base1 (b1) = 5 feetBase2 (b2) = 4 feetHeight (h) = 2.5 feetSubstitute these values into the formula:
Area = 1/2 × (5 + 4) × 2.5
Area = 1/2 × 9 × 2.5
Area = 4.5 × 2.5
Area = 11.25 square feet
Thus, the area of the trapezoid-shaped seat is 11.25 square feet.
Johanna wants to rent a car for 5 days, and she's interested in the loss damage waiver but not the collision damage waiver. If the daily rate is $29 and LDW totals $62 for the rental period, what is her total rental cost?
Answer:
$207
Step-by-step explanation:
yw
A coin is tossed 20 times. It lands on heads 14 times. What is the relative frecuencue of heads?
the ratio of red circles to blue circles is 1:3 How many more red circles would need to be added to make the ratio of red to blue 3:1?
how many 3s are in 1/8?
Answer:
less than 1
Step-by-step explanation:
1/8 can be translated to 0.125, multiply 0.125 by 3 to get 0.375.
What I think your assignment told you to do is calculate how many times 1/8 goes into 3 though, simply put, you just need to multiply 8 by 3 to find this result, which is 24.
A rectangular prism has a length of 2 1/2 meters, a width of 4 meters, and a height of 2 1/4 meters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
Please Help! Quickly!
Volume of rectangular prism is [tex]11\frac{1}{4}[/tex] cm³
Volume based problem;Given that:
Length of prism = [tex]2\frac{1}{2}[/tex] meter = 5/4 meter
Width of prism = 4 meter
Height of prism = [tex]2\frac{1}{4}[/tex] meter = 9/4 meter
Find:
Volume of rectangular prism = lbh
Volume of rectangular prism = [5/4][4][9/4]
Volume of rectangular prism = 45 / 4
Volume of rectangular prism = [tex]11\frac{1}{4}[/tex] cm³
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Suppose that you have 4 shirts (red, green, blue, yellow) and 3 pairs of shoes (black, brown, red). If you choose your shirt and shoes randomly, what is the probability that your shirt and shoes will NOT be the same color?
Which of the following had a graph that is wider than the graph of y=3x^2+2?
A. Y=3x^2+3
B. Y=0.5x^2+1
C. Y=-4x^2-1
D. Y=4x^2+1
Answer:
Out of the options given prior to the question, the graph that is wider than the graph y = 3x^2 + 2 would be B) y = 0.5x^2 + 1. Hope we helped! :D
Laila said 4 equals -4. Is Laila correct? Use the number line and words to support your answer
Tim fisher received a 1200 discount loan to purchase a computer the loan was offered at 18% for 180 days find the interest in dollars and the proceeds for the following problem
The interest is $106.30 and the proceeds is approximately $1093.70
Calculating simple interest.
The simple interest is the amount of interest charges on the amount being borrowed and its paid by the borrower.
The simple interest can be determined by using the formula;
[tex]S. I = \dfrac{p\times r \times t}{100}[/tex]
[tex]S. I = \dfrac{1200\times 18 \times \dfrac{180}{365}}{100}[/tex]
S.I = $106.30
The proceeds for the loan = Loan amount - interest
Proceeds = $1200 - $106.30
Proceeds = $1093.70
How do you do this obe
3. Janet is flying a kite on a string that is 75m long. The kite is 62m above the ground. Estimate the distance between Janet and the spot on the ground directly beneath the kite.
(a) Draw a diagram showing Janet and the kite.
(b) What is the length of the string of the kite?
Answer:
Please help I will reward brainly!! Please , will mark brainly please !
Answer:
Answer X = 67
Step-by-step explanation:
so what you do is
180 - 46 = 134
then you devide 134 by 2 which is
134/2 = 67
Answer X = 67
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What is 5(x+10)+x simplified
How do u find the mean? I've never done this before the subject is try check and revise
Answer,
The mean is the average of the numbers. It's quite simple to find the mean. All you do is, add all the numbers togter & divide by how many numbers there are. In simpler words, it is the sum divided by the count.
For example,
The mean of the numbers is, 50
Explanation,
20 + 30 + 40 + 50 + 60 + 70 + 80 = 380
Then we divide 350 by how many numbers there are, 7. Then we get 50.
Hope this helps :-)
how you would write an expression that shows the cost to rent the bicycle for d days.
Miki, a resident of Kyoto, earns an annual salary of ¥6,760,950. If the Japanese government levies a 29.12% income tax on Miki’s tax bracket, what is her yearly take-home pay, to the nearest whole yen?
Her yearly take-home pay, to the nearest whole yen is 4792161¥
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Miki, a resident of Kyoto, earns an annual salary of ¥6,760,950.
Since,
the Japanese government levies a 29.12% income tax on Miki’s tax bracket
Thus,
tax she pays = 6,760,950 *29.12%
tax she pays = 6,760,950 *29.12/100
tax she pays = 1,968,788.64¥
remaining income to take home = total income - tax
remaining income to take home = 6,760,950 - 1,968,788.64
remaining income to take home = 4792161.36¥
Therefore, her yearly take-home pay, to the nearest whole yen is 4792161¥
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Plot the following points on number line without measuring
To plot points on a number line without measuring, it needs to follow various points mentioned below.
What is a number line?A number line is a visual representation of the real number system, where every point on the line corresponds to a unique real number.
Here,
To plot points on a number line without measuring, you can follow these steps:
Repeat steps 4 and 5 for all the points you want to plot on the number line.
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