Answer:
(-10, 0) and (0,-5)
Step-by-step explanation:
For the function [tex]f(x)=-\dfrac{1}{2}x-5,[/tex] find x-intercept and y-intercept:
1. when y=0, then
[tex]0=-\dfrac{1}{2}x-5,\\ \\\dfrac{1}{2}x=-5,\\ \\x=-10;[/tex]
2. when x=0, then
[tex]y=-\dfrac{1}{2}\cdot 0-5,\\ \\y=-5.[/tex]
You get two points (-10, 0) and (0,-5). Plot them on the coordinate plane and connect, obtained line is the graph of the linear function [tex]f(x)=-\dfrac{1}{2}x-5.[/tex]
a maximum speed, and airplane travels 2460 miles against the wind in 6 hours. flying with the wind, the plane can travel the same distance in 5 hours
Answer:
for pluto answer is 451
Step-by-step explanation:
the legs of a isosceles right triangle both measures 10 inches find the lenth of the hypotenuse
Answer:
Step-by-step explanation:
You just add and subtract
An animal shelter had 9/10 of its crates filled with animals. 1/2 of the filled crates are holding dogs.What fraction of the total number of crates are holding dog?
Answer:
9/20
Step-by-step explanation:
9/10 times 1/2 equals 9/20
Answer:
9/20
Step-by-step explanation:
3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000i in decimal form
Answer:
3030.033
Step-by-step explanation:
Multiply each piece out and add them together
3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000
3000 + 30+.03 + .003
3030.033
Using the given scale factor and center dilate the following figures and state the new coordinates
Answer:
B' = (-8,-1) , C' = (4, 5)
Step-by-step explanation:
The coordinates of A are (-5,-7)
The coordinates of C are 3 units to the right and 4 up from A.
So for a dilation factor 3 C' will be 9 to the right and 12 up from A.
C' = (-5 + 9) , (-7 + 12)
= (4, 5).
The point B is 1 unit to left and 2 up from A.
So B' is (-5 -3) , (-7+ 6)
= (-8, -1).
After a dilation scale factor of 3 centered at A, B'(- 18, - 15), and C'(- 6, - 9).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A triangle ABC.
The coordinate of B is (- 6, - 5), and the coordinate of C is (- 2, - 3).
After a dilation scale factor of 3 centered at A coordinates of B' would be
(- 6×3, - 5×3) = (- 18, - 15) and C'(- 2×3, - 3×3) = (- 6, - 9).
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A football team lost 3 yards on the first play in 6 yards on their second play. How many total yards did they lose?
Answer:-11
Step-by-step explanation:
use -6 to represent losing 6 yards
use -5 to represent losing 5 yards
add these together
(-6) + (-5) = -11
when adding two negative values, make sure your sum is negative
Answer:
it is 9
Step-by-step explanation:
6 plus 3 is 9
I had this for homework so I know
each roll of tape is 30.5 feet long. a box contains 454 rolls of tape. in total, there are _ yards
Answer:
4617 yd
Step-by-step explanation:
30.5 ft make 1 roll of tape
Length of tape = 454 × 30.5/1
Length of tape = 13 847 ft
1 ft = 3 yd
Length of tape = 13 847 × 1/3
Length of tape = 4617 yd
Peter calculated that the theoretical probability of obtaining exactly two heads when flipping six coins is 23.4%. What number of heads also has a 23.4% theoretical probability of coming up when 6 coins are flipped?
Answer:
4 heads
Step-by-step explanation:
Assuming the coins are properly weighted such that each side is equally likely, this means that getting heads is the same probability as getting tails. We're told that getting 2 heads and 4 tails is a 23.4% chance. If we somehow fool our brains into thinking heads and tails swap, then it would be 4 heads and 2 tails. The swap is simply changing the labels for each coin. It really doesn't matter. This symmetry is useful to help simplify larger problems.
If the coins were altered so that the chances of getting heads on any single coin toss was something like 60%, then swapping the labels wouldn't work because the two sides would be different.
Help me with question 15 plz?
Answer:
B
Step-by-step explanation:
well plug in x and y
so if it says y=2x-3 put it as 7=(2x2)-3 and see if it gives u 7 and if it does di the next set of x and y numbers
Answer:
B y=2x+3
Step-by-step explanation:
We need to find the slope of the relationship in the table
m = (y2-y2)/(x2-x1)
= (13-7)/(5-2)
= 6/3
=2
The slope is 2
We can use point slope form to make an equation
y-y1=m(x-x1)
y-7 = 2(x-2)
Distribute the 2
y-7 =2x-4
Add 7 to each side
y-7+7 =2x-4+7
y = 2x+3
What is the equation of a line with a slope of −4 and a point (−2, 5) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Enter your answer in the box.
Expressing the equation in the form y = mx + b where m is slope and b is y-
intercept is represented as y = -4x - 3
The slope intercept form is represented as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
m = -4
using the coordinate (-2, 5) lets find b
y = -4x + b
5 = -4(-2) + b
5 = 8 + b
b = 5 - 8
b = -3
Therefore,
y = -4x - 3
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I AM GIVING 10 POINTS TO WHOMEVER ANSWERS THIS!!!
Simplify: 9^-5 × 9^-3
A) 1/9^8
B) 1/9^2
C) 9^8
D) 9^15
Answer:
A) (1/9)^8
Step-by-step explanation:
9^-5 × 9^-3 =
Rule: a^m * a^n = a^(m + n)
= 9^-8
Rule: (a^m)^n = a^(mn)
= (9^-1)^8
Rule: a^-m = 1/a^m
= (1/9)^8
Answer: A) (1/9)^8
Find the constant of proportionality (r)in the equation y=rx.
r =
Answer:
Constant of proportionality, [tex]r = \frac{1}{10}[/tex]
Step-by-step explanation:
Constant of proportionality states that the constant value of the ratio of two proportional quantities x and y,
it is written in the form of y = kx, where k is the constant of proportionality.
Given the equation: [tex]y =rx[/tex] .....[1]
where r is the constant of proportionality.
From the table we consider
x = 14 and y = 1.4
Substitute these given values in [1] to solve for r;
[tex]1.4 = r(14)[/tex]
Divide both sides by 14 we get;
[tex]r = \frac{1.4}{14} = \frac{14}{140} = \frac{1}{10}[/tex]
therefore, the Constant of proportionality, [tex]r = \frac{1}{10}[/tex]
The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x.
Explanation:The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x. For example, in the equation y = rx, 'r' represents how much y changes for every unit change in x.
For instance, if the equation is y = 2x, then the constant of proportionality is 2. This means that for every unit increase in x, y increases by 2 units.
Keywords: constant of proportionality, linear equation, rate of change
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Write the quadratic equation whose roots are 6 and -5, and whose leading coefficient is 3
To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.
Explanation:The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5).
Expanding this, we have:
3(x² + 5x - 6x - 30)3(x² - x - 30)3x² - 3x - 90The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.
What number comes between 2 and 4
Answer:
3
Step-by-step explanation:
Count 1 to 5 (1,2,3,4,5). You can see 3 is between 2 and 4.
A number that comes between 2 and 4 would be 3.
Used the concept of a number system that states,
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Given that,
Two numbers are 2 and 4.
Let us assume that the number that comes between 2 and 4 is, x
Then,
[tex]x = \dfrac{(2 + 4)}{2}[/tex]
[tex]x = \dfrac{(6)}{2}[/tex]
[tex]x = 3[/tex]
Therefore, the number would be 3 which comes between 2 and 4.
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A publishing company is going to have 24,000 books printed. There are between 3 and 4 books out of ever 3,000 that will have a printing error. At this rate, which number could be the exact number of books that will have a printing error? a. 7 b. 12 c. 31 d. 36
Answer:
C. 31
Step-by-step explanation:
3000 there are 3-4 errors
If we first divide 24,000 by 3,000, will get 8
then since there a error for each 3,000 books, we do 8 x 4 = 32 and 8 x 3 = 24
32 (8 x 4) the max amount of printing errors
24 (8 x 3) the minimum amount of printing errors
So we should expect 24-32 printing errors
Only answer between the numbers is c. 31
Final answer:
The exact number of books that could have a printing error out of 24,000, given the rate of 3 to 4 errors per 3,000 books, can be calculated to be within a range, making 31 the only viable option provided.
Explanation:
The question is about determining the exact number of books that will have a printing error out of 24,000, given that there are between 3 and 4 printing errors per every 3,000 books. To find the possible number of errors, we multiply the number of books (24,000) by the rate of errors (3 to 4 per 3,000). This gives us a range of possible errors, from (24,000 / 3,000) * 3 = 24 to (24,000 / 3,000) * 4 = 32. Therefore, the only option within this range is 31.
How much of a spice that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt?
Please Helpppp!!
Answer:
Let y represents the ounces of first spice.
From the given statements, we draw a table as shown below:
ounces of spice Percentage ounces of salt
First spice y 3% 0.03x
Second spice 175 6% 175(0.06)
Final mixture y + 175 5% (x+15)(0.05)
Now, to solve for y
we have;
Final spice = First spice + second spice
[tex]0.03y + 175(0.06) = (y+175)(0.05)[/tex]
[tex]0.03y+ 10.5= 0.05y+ 8.75[/tex]
Subtract 10.5 on both sides we have;
[tex]0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5[/tex]
Simplify:
[tex]0.03y = 0.05y -1.75[/tex]
Subtract 0.05y on both sides
[tex]0.03y -0.05y= 0.05y -1.75-0.05y[/tex]
Simplify:
[tex]-0.02y = -1.75[/tex]
Divide both sides by -0.02, we get;
[tex]y = \frac{-1.75}{-0.02} = 87.5[/tex]
Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt
It needs 87.5 ounces of spice that is 3% salt.
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
[tex]\texttt{ }[/tex]
Given:
175 ounces of a spice that is 6% salt
[tex]\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
x ounces of a spice that is 3% salt
[tex]\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
(175 + x) ounces of a spice that is 5% salt
[tex]\texttt{total mass of salt} = s_1 + s_2[/tex]
[tex]5\% \times ( 175 + x ) = 10.5 + 0.03x[/tex]
[tex]8.75 + 0.05x = 10.5 + 0.03x[/tex]
[tex]0.05x - 0.03x = 10.5 - 8.75[/tex]
[tex]0.02x = 1.75[/tex]
[tex]x = 1.75 \div 0.02[/tex]
[tex]x = 175 \div 2[/tex]
[tex]x = 87.5 \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
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Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3
Find the equation of the circle with center at (3, 2) and through the point (5, 4).
Answer:
(x - 3)² + (y - 2)² = 8
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre to a point on the circle
To find r use the distance formula
r = √(x₂ - x₁)² + (y₂ - y₁)²
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)
r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]
(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²
(x - 3)² + (y - 2)² = 8 ← equation of circle
Tess left her home and drove for 3.7 hours due north at a rate of 60 miles per hour. After attending a concert, she drove due south for 1.4 hours at 55 miles per hour.
How far is Tess from her home?
Answer: 145
3.7 x 60 = 222 (how far north she drove)
1.4 x 55 = 77 (how far south she drove)
222 - 77 = 145 (how far from home)
Multiply.
Express the product in simplest form.
3/9·18=b
2
6
154
5
Answer:
The answer is 6
Step-by-step explanation:
What you do is this.
3/9 times 18/1 because you need to make 18 a fraction and then multiply. And you will get 6
PLEASE HELP! I will award brainliest to the most helpful answer. I need an in depth explanation, not just the answer. How do you know which side to shade/ where to shade? Thank you so much!
Answer:
y ≤ -4x+25
Step-by-step explanation:
First we need to figure out the equation for the line
The y intercept is 25
Next figure out the slope
slope = (y2-y1)/((x2-x1)
= (49-25)/(-6-0)
= 24/-6
= -4
The equation for a line in slope intercept form is y = mx+b
y = -4x+25
This is a solid line so our inequality will have an equals in it.
It is shaded below, so y is less than.
If it was shaded above, y would be greater than
y ≤ -4x+25
The area of a rectangle is 27 square meters. If the length is 6 meters less than 3 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth
Answer:
width = 4.16 meter
length = 6.49 meter
Step-by-step explanation:
Area of the rectangle =27 m²
Let the width of the rectangle be x meter
So, Length = 3 * width - 6
= 3*x - 6
= 3x-6 meter
Area of the rectangle = length * width
27 = (3x-6)*x
Flipping the sides of the equation, we have
(3x-6)*x =27
Distributing the left side, we get
(3x)*(x) - (6)*(x) = 27
=> 3x² - 6x = 27
Subtract 27 from both sides,
3x² - 6x -27 = 27 - 27
=> 3x² - 6x -27 = 0
Factoring out 3 from all the terms on the left side, we have
3(x² - 2x -9) = 0
Dividing both sides by 3, we have
[tex]\frac{3(x^{2}-2x-9) }{3}[/tex] = [tex]\frac{0}{3}[/tex]
Cancelling out the 3's on the left, we get
x² - 2x -9 = 0
We'll use the quadratic formula to solve for the x,
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Comparing the quadratic equation x² - 2x -9 = 0 with ax² + bx + c = 0, we get
a = 1 (as x² has no coefficient)
b = -2
c = -9
Plugging in the values of a, b, and c into the quadratic formula, we get
x = [tex]\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-9) } }{2(1)}[/tex]
=> x = [tex]\frac{2\pm\sqrt{4+36 } }{2}[/tex]
=> x = [tex]\frac{2\pm\sqrt{40}}{2}[/tex]
=> x = [tex]\frac{2\pm2\sqrt{10}}{2}[/tex]
Factoring out 2 from the top, we get
x = [tex]\frac{2(1\pm\sqrt{10})}{2}[/tex]
Canceling out the 2's from the top and bottom, we have
x = [tex]1\pm\sqrt{10}[/tex]
Either x = [tex]1+\sqrt10[/tex] or x= [tex]1-\sqrt10[/tex]
=> x = 1 + 3.162 or x = 1 - 3.162
=> x = 4.162 (possible) or x = -2.162 (not possible as width can't be negative)
So, width = 4.16 meter (rounded off to the nearest hundredth)
Now,
Area of the rectangle = length * width
27 = length * 4.16
Flipping the sides of the equation,
length * 4.16 = 27
Dividing both sides by 4.16, we get
[tex]\frac{length * 4.16}{4.16} = \frac{27}{4.16}[/tex]
Cancelling out 4.16 from the top and bottom of the left side, we get
length = 6.490
=> length = 6.49 meter (rounded off to the nearest hundredth)
What is 25% of $1200?
A) 900
B) 250
C) 600
D) 300
Answer:
The answer Is D
Step-by-step explanation: I looked it up on Google, next time just type it into Google because it will solve it on a calculator for you.
Answer: It is choice D
Step-by-step explanation: To figure out 25% of 1,200, multiply 1,200 by 0.25. 1,200 x 0.25 = 300
Which expressions represent 1 more then the product 5 and 2
Answer:
1+5*2 or simplified, 1+10= 11
George spun a 6 sided spinner that had colors blue, red, white, yellow, black, and purple. She landed on blue-3 times, red-4-times, white-3 times, yellow-2 times, black-5 times, and purple-1 time. What is the experimental probability that George will spin a red then a yellow?
Answer:
[tex]\frac{2}{81}[/tex]
Step-by-step explanation:
Step 1
List the experimental probabilities of each color using the first letter of that color. The spinner is spun 18 times The probabilities are listed below. P(blue)=3/18, P(red=4/18), P(white) =3/18, P(yellow)=2/18, P(black)=5/18, P(purple)=1/18
Step 2
The second step is to calculate the required probability given the information in step 1. The probability that George will spin a red and then a yellow is obtained by multiplying the probability that he spins a red and the probability that he spins a yellow. This calculation is shown below,
[tex]P=P(red)\times P(yellow)=\frac{4}{18} \times \frac{2}{18} =\frac{8}{324} =\frac{2}{81}.[/tex]
The correct answer is [tex]\frac{2}{81}[/tex]
PLEASE HELP ASAP! I don’t know how to do this can someone please help.
Answer: 2.50
Step-by-step explanation: your answer is 2.50
please help???????????
Answer:
x - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
A polynomial has the form
first term is the term of highest degree followed by term of second etc.
note that x = [tex]x^{1}[/tex] ← degree 1
x - [tex]\sqrt{7}[/tex]
fits this description and is a polynomial of degree 1
3/7-2/14 (8-1/2) +2/7
what is the domain of the function in this table? X 3 4 5 6 Y 4 4 2 5
Answer:
The domain is {3,4,5,6}
Step-by-step explanation:
Because all your x - values is ur domain and ur y - values is ur range
Please help What is the equation of a line with a slope of −4 and a point (−2, 5) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have m = -4 and the point (-2, 5). Substitute:
[tex]y-5=-4(x-(-2))[/tex]
[tex]y-5=-4(x+2)[/tex] use distributive property
[tex]y-5=(-4)(x)+(-4)(2)[/tex]
[tex]y-5=-4x-8[/tex] add 5 to both sides
[tex]\boxed{y=-4x-3}[/tex]
Answer:
all is work is shown and pictured
Match the following reasons with the statement givem
Answer:
AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent
In triangle RAS and triangle QAT
[tex]\angle R =\angle Q[/tex] [Angle]
[tex]AS =AT[/tex] [Side] [Given]
By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.
⇒ [tex]\angle 5= \angle 6[/tex] [By base ∠'s of isosceles triangle are equal]
By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.
[tex]\angle 4[/tex], [tex]\angle 5[/tex] are supplementary and [tex]\angle 6[/tex], [tex]\angle 7[/tex] are supplementary.
⇒[tex]\angle 4+ \angle 5 =180^{\circ}[/tex] and
[tex]\angle 6+ \angle 7 =180^{\circ}[/tex]
Two [tex]\angle 's[/tex] supplementary to equal [tex]\angle 's[/tex]
[tex]\angle 4+ \angle 5 =\angle 6+ \angle 7[/tex]
Since, [tex]\angle 5 =\angle 6[/tex]
then, we get;
[tex]\angle 4 =\angle 7[/tex] [Angle]
then, by AAS postulates,
[tex]\triangle RAS \cong \triangle QAT[/tex]
By CPCT[Corresponding Part of Congruent Triangles are equal]
[tex]RS = QT[/tex] Hence Proved!