Answer:
The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].
Step-by-step explanation:
A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).
It is asked to find a linear equation satisfying the given condition.
To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.
Step 1 of 2
Determine the slope of the line.
The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
[tex]$$y=m x+b$$[/tex]
The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.
So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,
[tex]$y=\frac{4}{5} x+4$$[/tex]
This is the required linear equation.
A card is drawn at random from a standard 52-card deck. What is the probability that it is an odd number (3,5,7,9) or a $\spadesuit$ (or both)
The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
In the question, we are informed that a card is drawn at random from a standard 52-card deck.
We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.
We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.
The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4*4 = 16}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event A, P(A) = 16/52.
The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event B, P(B) = 13/52.
The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.
The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.
Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
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Which quadratic equation is equivalent to (x-4)² – (x − 4) − 6 = 0?
A)O (u-4)2-(u-4)-6=0
where u = (x-4)
B)Ou²-(u-4)-6=0
where u = (x-4)
C)Ou²-16-u-6=0 where u = (x-4)
D)Ou²-u-6=0 where u = (x-4)
The quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
(x-4)² – (x − 4) − 6 = 0
Let (x - 4) = u
u² - u - 6 = 0
Thus, the quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.
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Answer:Option D on edge 2022
Step-by-step explanation:
One pipe fills a barrel in 1 hour while another pipe can fill the same barrel in 2 hours. How many minutes will it take to fill the tank if both pipes are used
It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.
Let pi be pipe 1 and pi2 be pipe 2
pi = 1 / 1
pi2 = 1 / 2
together = 1/1 + 1/2 ;
3/2 time ; 2/3 hour.
It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.
Problem-solving is the act of defining a problem; figuring out the motive of the problem; identifying, prioritizing, and deciding on alternatives for a solution; and implementing an answer.
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Find the Value of X!!! Geometry!! Pls helppp!! I will mark brainlest. Thank you!! :)
What is the measure of angle CED?
There are two triangles labeled ABC and DCE with a common vertex C. In triangle ABC, angle BAC is labeled as p, and angle ABC is labeled as 70 degrees. In triangle DCE, angle CDE is labeled as 70 degrees.
please help!!!
Answer Choices- p over 2, because Triangle ABC is congruent to triangle DCE
p + 70 degrees, because Triangle ABC is similar to triangle DCE
110 degrees − p, because Triangle ABC is congruent to triangle DCE
p, because Triangle ABC is similar to triangle EDC
Answer:
p, because Triangle ABC is similar to triangle EDC
Step-by-step explanation:
Angles DCA and DCE are vertical, so they are congruent.
Angles ABC and CDE measure 70°, so they are congruent.
Triangles BCA and DCE are similar by AA Similarity.
By corresponding angle of similar triangles, angles CED and BAC are congruent.
m<BAC = p
m<CED = m<BAC = p
m<CED = p
A parobola has the equation y=x²+2x-3
What are the coordinates of the turning point of the parabola? what is the equation of the axis of symmetry for this parabola?
Answer:
(-1,-4) is the vertex
x = -1 is the equation of symmetry;
Step-by-step explanation:
See attached image.
Answer:
(- 1, - 4 ) and x = - 1
Step-by-step explanation:
given a parabola in standard form
y = ax² + bx + c ( ax≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 2x - 3 ← is in standard form
with a = 1, b = 2 , then
x = - [tex]\frac{2}{2}[/tex] = - 1
substitute x = - 1 into the equation for corresponding y- coordinate
y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4
vertex = (- 1, - 4 )
this is an upward opening parabola ( a > 0 )
the axis of symmetry is a vertical line passing through the vertex with equation
x = c ( c is the value of the x- coordinate of the vertex ), then equation is
x = - 1
The largest possibly circle has been cut from a piece of paper.what is the area of the remaining area . caculate the area of just one side of the remaining paper.use 3.14 for the value of pi.
22/7 was considered while choosing the square's side length, the area of just one side of the remaining paper which is a multiple of 7.
Calculate the area of just one side of the remaining paper. use 3.14 for the value of pi.Since the largest circle that can be encircled by a square has a diameter "d" equal to its side length, we may use "d" to conveniently calculate both the square's area and the circle's area.
The largest possibly circle has been cut from a piece of paper.
Square’s area = [tex]d^2[/tex]
Circle’s area =ᴨ[tex]d^2/4[/tex]
Simplifying-
(divide both area by [tex]d^2[/tex]) we find their ratio is 1:(ᴨ/4) or 4/ᴨ (square: circle), and the inverse, ᴨ/4 circle: square.
Therefore diameter of circle =14 cm.
Hence area of circle=πr2.
If you use 22/7 as an approximation for ᴨ, the circle’s area 22/28 of the square’s, the square’s area is 28/22 of the circle’s , it follows that the area outside the circle is (28–22)/28 of the square’s area, which is (28–22)/28 x 14 x14,
or 6/28 x 14 x 14,
or 3/14 x 14 x 14,
or 42 square inches or-
(4-ᴨ)/4 x 14 x 14
22/7, It's a rather accurate estimate.
22/7 was considered while choosing the square's side length, which is a multiple of 7.
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I need help I’ll give branliest
Answer:
A
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
we know the thickness is x, so the sides are 3+2x and 4+2x
then we use foil:
(3+2x)(4+2x)=12+6x+8x+4x^2=4x^2+14x+12
we know the area is 15
4x^2+14x+12=15
4x^2+14x-3=0
So it is B
Sum of two digits is 8. When the digits are reversed, the number increased by 36. Find the number.
Answer:
26
Step-by-step explanation:
Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.
The sum of the two digit number is 8: x+y=8
When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36
Now we have two equations and two unknown parameters, so we have enough information to find those parameters.
Solve for x:
X=8-y
plug in x:
(10y + 8-y) - (10(8-y)+ y) = 36
simplify:
(9y + 8) - (80-9y) = 36
18y - 72 = 36
y = 108/18 = 6
so if y=6, then x=8-y=8-6=2
so our number is 26. 62 is 36 greater than 26.
Tell what shape is created by each cross section...
The shapes from the cross section are square, parallelogram, trapezium, kite, triangle and rectangle.
Shapes formed from the cross sectionIt is important to note that the cross section of a cube is a square.
From the cross section visible from the figure, we have the shapes;
squareParallelogramTrapeziumTriangleKiteRectangleThus, the shapes from the cross section are square, parallelogram, trapezium, kite, triangle and rectangle.
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HELP HELP HELP
HELP HELP HELP
Answer:
$9.92 (rounded off to nearest cent)
Step-by-step explanation:
Square of 7-inch radius pizza = [tex]7^{2}[/tex] = 49 inches
49 Inches = $6
Square of 9-inch radius pizza = [tex]9^{2}[/tex] = 81 inches
Given 49 Inches = $6
1 inch =$ [tex]$(\frac{6}{49} \\)[/tex]
I will leave it as a fraction as it is not the final answer, rounding it off will result in a loss of accuracy.
81 Inches = [tex]81* \frac{6}{49} \\[/tex]
= $9.92 (rounded off to nearest cent)
Simplify, Write your answer in exponential notation.
a.) 2³ x 2-5
b.) (602)3
The simplified expressions are 2^-2 and 60^6
How to simplify the expressions?Expression (a)
We have:
2^3 * 2^-5
Apply the product law of indices
2^3 * 2^-5 = 2^(3 - 5)
Evaluate the difference
2^3 * 2^-5 = 2^-2
Expression (b)
We have:
(60^2)^3
Apply the power law of indices
(60^2)^3 = 60^(2 * 3)
Evaluate the product
(60^2)^3 = 60^6
Hence, the simplified expressions are 2^-2 and 60^6
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Starting with the graph of f(x) = 5, write the equation of the graph t
a) f(x) is shifted 2 units downward.
b) f(x) is shifted 9 units to the left.
c) f(x) is reflected about the y-axis.
d) f(x) is shifted 3 units upward and 7 units to the right.
The graphs of the transformations in each case are as follows;
a) f(x) = 5 -2 = 3
b) f(x) = 5
c) f(x) = 5
d) f(x) = 5+3 = 8.
What are transformations?The shifts, reflections, rotations and dilation operations are facilitated by transformation operations. On this note, it therefore follows that the graph of the given function as given is a straight horizontal line which is parallel to the x-axis and consequently, the transformations are as given above.
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Suppose y varies directly with x and y=76 when x=19 what is the value of x when y = "-32
The value of y = -32 , x = -8 .
What is the meaning of Direct Variation ?Direct Variation is when a variable is dependent on the other variable such that , on increasing one variable the other also increases.
It is given that
x and y are two variables
and they are in direct variation
y ∝ x
y = k x
where , k is the proportionality constant
From the given data , y = 76 when x = 19
76 = k * 19
k = 4
The value of x , when y = -32
-32 = 4 * x
x = -8
Therefore for y = -32 , x = -8 .
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Recovery
Solve the one-variable equation using the distributive property and properties of equality.
-6(2 + a) = -48
What is the value of a?
O a = -6
O a=-3
O a=5
O a=6
g An empty plastic or glass dish being removed from a microwave oven can be cool to the touch, even when food on an adjoining dish is hot. How is this phenom- enon possible?
The plastic and the glass contain no water molecules. Plastic and glass have very different absorption frequencies from water, so they may not absorb any significant microwave energy and remain cool to the touch.
The absorption of electromagnetic radiation by water depends on the state of the water.
The absorption in the gas phase occurs in three regions of the spectrum. Rotational transitions are responsible for absorption in the microwave and far-infrared, vibrational transitions in the mid-infrared and near-infrared. Vibrational bands have rotational fine structure. Electronic transitions occur in the vacuum ultraviolet regions.
It is given that an empty plastic or glass dish being removed from a microwave oven can be cool to the touch, even when food on an adjoining dish is hot.
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eric borrowed 5,000 to buy a used car. he agreed to make monthly payments of 175.00 for 36 months how much will how actually pay the bank
The actual payment Eric made to the bank at 175.00 for 36 months is 6,300
Actual paymentAmount borrowed = 5,000Monthly payment = 175.00Number of months = 36Actual payment to bank = Monthly payment × Number of months
= 175.00 × 36
= 6,300
Therefore, the actual payment made to the bank is 6,300.
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Simplify the expression.(2b/3)^4
Step-by-step explanation:
the solution is in the photo I sent
!!!!!!!!!HELLLLLPPPP!!!!!!
Find the maximum and minimum values. You will want to draw a graph to determine the intersections of the constraints below.
f=2x + 5y, subject to the constraints
3x + 2y ≤ 6,
-2x + 4y ≤ 8,
x 20,
y 20.
12-²
Maximum: 4: Minimum: 4
12-
Maximum: 4: Minimum: 0
Maximum: 10; Minimum: 0
13-
Maximum: 4: Minimum: 0
Answer:
maximum 4 Mimimum I'm 0 or maximum 10 minimum 0
The orthodontist estimated how long brian would have to wear braces when she put them on his teeth. brian was pleasantly surprised when, after 16 months, the orthodontist said it was time to take the braces off. her original estimate had been 12.5% longer than that. how long was the original estimate?
Using the given information, the original estimate was 18 months
PercentagesFrom the question, we are to determine how long the original estimate was
Let the original estimate the x
Then, from the given information, we ca write that
x = 16 + (12.5% × 16)
x = 16 + (0.125 × 16)
NOTE: 12.5% = 12.5/100 = 0.125
∴ x = 16 + 2
x = 18
Hence, the original estimate was 18 months
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Cheryl plans to bake cookies tomorrow and needs to purchase chocolate chips and pecans for no more than $25 total. Chocolate chips are $2 per pound and pecans are $5 per pound. Which of the following graphs correctly represents the scenario?
The inequality that correctly represents this scenario is given as follows:
[tex]2x + 5y \leq 25[/tex]
The graph is given at the end of the question.
What is a system of inequalities?A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: number of chocolate chips purchased.Variable y: number of pecans sold.Chocolate chips are $2 per pound and pecans are $5 per pound. She wants to spend at most $25, hence:
[tex]2x + 5y \leq 25[/tex]
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Find the loss or gain % when 20 pens are sold for the CP of 25 pen.
Answer:
20% gained
Step-by-step explanation:
25 - 20 = 5
5 / 25 * 100 = 20%
The table represents some points on the graph of a linear function.
Which function represents the same relationship
Answer:
Step-by-step explanation:
Which statement completes this proof
The answer to this question is A
A fish tank with a rectangular base has a volume of 3360 cubic inches. the length of the tank is 14 inches and the width is 12 inches. the height of the tank is 20 inches. if one fluid ounce is 1.8 cubic inches how much water will the tank hold ? your answer should be in gallons.
Answer:
14.58 gallons
Step-by-step explanation:
The tank volume is 3360 in^3, which is the product of the base x length x height (14)(12)(29) = 3360 in^3.
We are given a conversion factor: 1 fluid oz = 1.8 in^3
We can write this as (1 fluid oz)/( 1.8 in^3).
Use this conversion factor to confert volume to fluid oz:
(3360 in^3)*((1 fluid oz)/( 1.8 in^3)) = 1867 fluid oz
There are 128 fluid oz/gallon. Make this into a conversion factor:
(1 gallon/128 fluid oz) [The conversion factor can be written with oz or gallon on the top - it makes no difference since the two values are equal to each other]
(1867 fluid oz)*((1 gallon/128 fluid oz) = 14.58 gallons
water the tank will hold = 14.583 gallons
What is cuboid ?A cuboid is a three-dimensional or solid shape. A cuboid is a convex polyhedron that has six rectangular faces, eight vertices, and twelve edges. Another name for a cuboid is a rectangular prism. A cube is a cuboid with six square faces. The basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.
Given : A fish tank has a volume = 3360 cubic Inches.
The length of the tank is =14 inches
the width is = 12 inches.
The height of the tank is = 20 inches.
If one fluid ounce is = 1.8 cubic inches
Volume of tank = 14 * 12 * 20 = 3360 cubic inches
1.8 cubic inches = one fluid ounce
3360 cubic inches = 3360/1.8 fluid ounce
= 5600/3 fluid ounce
As we know,
1 gallons = 128 fluid ounces
water the tank will hold =( 5600/3 ) / 128
= 175 / 1 = 14.583 gallons
Therefore, water the tank will hold = 14.583 gallons
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My son graduated and we no longer need this service. however, since we have not used it in a couple years we forgot names/passwords. how do we cancel and stop being charged? thanks eamonn burgraff
Answer:
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HELP HELP HELP!!!
How many degrees is arc ZY?
How many degrees is angle YXZ?
Line XZ is a diameter of the circle. How many degrees is arc XYZ?
How many degrees is arc XY?
(Picture is attached below. Thank you)
Part 1
By the inscribed angle theorem, arc ZY measures 76 degrees.
Part 2
Since angles inscribed in the same arc are congruent, angle YXZ measures 38 degrees.
Part 3
Since diameters form semicircles and the arc of a semicircle measures 180 degrees, arc XYZ measures 180 degrees.
Part 4
Subtracting arc ZY from arc XYZ, we get 104 degrees.
What does the author predict about the future of the Earth's mantle? Do you support his educated guess? Use complete sentences to answer.
The prediction of the author about the future of the earth's mantle is that it would affect the sea level rise.
What is a Prediction?This refers to the statement that contains a forecast about future events that is made.
Hence, we can see that from the complete text, there is the scientific explanation of the lead researcher about the future of the Earth's mantle and how this would affect sea levels as they would increase.
Yes, I support his guess because he made use of past events and current happenings to show the effects on the sea levels.
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How many different "words" can be made from the given word by re -arranging the
letters?
KINDNESS
(don't have to be real words)
Find the solutions of the quadratic equation 2x² + 6x - 2 = 0.
Choose 1 answer:
A: -3/2 + or - sqrt of 13 / 2 • i
B: -3/2 + or - sqrt of 13 / 2
C: -3/4 + or - sqrt of 13 / 2
D: 3/2 + or - sqrt of 13 / 2