The values of the slope and y-intercept are m=8 and b=−25
m=8
b=−25
To find the slope you would use the slope formula since you have two point coordinates. The slope formula is:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where y2 and y1 are the y coordinates of the two points and x2 and x1 are the x coordinates of the two points.
Substitute in 7 and -1 for y2 and y1; substitute in 4 and 3 for x2 and x1. Now your expression should look like:
[tex]\frac{7-(-1)}{4-3}[/tex]
Subtract -1 from 7, which is basically the same as 7 + 1. Then subtract 3 from 4. Once you complete these steps you can rewrite your fraction.
[tex]\frac{7+1}{4-3} =\frac{8}{1} =8[/tex]
The final answer is 8 after substituting the appropriate coordinates into the slope formula. This means that the slope of the line passing through the points (3, -1) and (4, 7) is 8.
The answer is: the slope of the line is 8.
Select the postulate of equality or inequality that is illustrated. If One Fourths (1/4) + One Fourths (1/4) = Two Fourths (2/4) and Two Fourths (2/4) = One Half (1/2), then One Fourth (1/4) + One Fourth (1/4) = One Half (1/2)
Answer:
'Transitive postulate of equality'
Step-by-step explanation:
To find : The postulate of equality or inequality that is illustrated.
Solution :
Given illustration is
[tex]\frac{1}{4}+\frac{1}{4}=\frac{2}{4}[/tex] and [tex]\frac{2}{4}=\frac{1}{2}[/tex]
Then, [tex]\frac{1}{4}+\frac{1}{4}=\frac{1}{2}[/tex]
Now, We let [tex]\frac{1}{4}+\frac{1}{4}=a,\frac{2}{4}=b,\frac{1}{2}=c[/tex]
According to this, [tex]a=b\text{ and }b=c\text{ then }a=c[/tex]
Which is 'Transitive postulate of equality'.
So, The required postulate of equality is transitive.
The equation 'One Fourth (1/4) + One Fourth (1/4) = One Half (1/2)' illustrates the Transitive Property of Equality. This mathematical property states that if 'a' equals 'b' and 'b' equals 'c', then 'a' must also equal 'c'. In this case, 'a' is '1/4 + 1/4', 'b' is '2/4', and 'c' is '1/2'.
Explanation:The mathematical postulate illustrated by the equation One Fourth (1/4) + One Fourth (1/4) = One Half (1/2) is the Transitive Property of Equality. In mathematics, the transitive property states that if a = b and b = c, then a = c. In this case, 'a' is One Fourth (1/4) + One Fourth (1/4), 'b' is Two Fourths (2/4), and 'c' is One Half (1/2). Because it has been established that 'a' equals 'b' (1/4 + 1/4 = 2/4) and 'b' equals 'c' (2/4 = 1/2), the Transitive Property of Equality allows us to conclude that 'a' equals 'c' (1/4 + 1/4 = 1/2).
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You earn $ 20 per hour doing landscaping work . Your total earnings depend on the amount of hours you spend landscaping .
Part A: What is the independent variable?
Part B: What is the dependent variable?
Part C: Write a function to represent the situation.
A: Amount of hours (h) you spend landscaping
B: Earnings ($20)
C: h(20)= 20^h
The three angles of a triangular sail have a sum of 180°. The largest angle measures 90° and the smallest angle measures x°. In degrees, which expression shows the measure of the third angle?
The measure of the third angle in the triangular sail, given that the largest angle is 90° and the smallest angle is x°, is found by subtracting the known angles from 180°, giving the expression 90° - x°.
Explanation:In a triangular sail, the sum of all the angles totals to 180°. Given that the largest angle measures 90° and the smallest angle measures x°. We find the measure of the third angle by using the fact that the sum of angles in a triangle equals 180 degrees. Therefore, if we subtract the two known angles from 180, we can locate the measure of the third angle. So the expression to determine the third angle in degrees would be 180° - 90° - x°, simplifying the expression to 90° - x°.
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What does it mean if a check was skipped on a bank statement? A. The check may not have been cashed or deposited yet. B. The check was written for more money than was available in the account. C. The account holder wasted money by not using a check. D. The bank will charge a fee for the skipped check.
Answer:
A. The check may not have been cashed or deposited yet.
Step-by-step explanation:
Our bank statements contains all our transactions like the debits or withdrawals, credits or deposited amounts and checks deducted etc.
And all the transactions are ordered date wise.
So, if a check was skipped on a bank statement, that means the check has not been cashed yet.
Answer:
A for plato
Step-by-step explanation:
In an acute angled triangle ABC sin 2(A+B-C) = 1 and tan(B + C -A) =√3, then find the values of A, B and C
Given
In an acute angled triangle ABC .
sin 2(A+B-C) = 1
tan(B + C -A) =√3
To proof
As given in the question
In an acute angled triangle ABC .
first solving the equation
sin 2(A+B-C) = 1
[tex]2 ( A + B - C ) = sin^{-1} (1)[/tex]
As we know
1 = sin90°
put this in the above equation
we get
[tex]2 ( A + B - C ) = sin^{-1} (sin90^{\circ})[/tex]
2A + 2B - 2C = 90
A+B -C =45 ( first equation )
now solving the equation
we get
tan(B + C -A) =√3
[tex]B + C -A =tan^{-1} \sqrt{3}[/tex]
[tex]B + C -A =tan^{-1}(tan60^{\circ})[/tex]
B + C -A = 60 ( second equation )
As given acute angled triangle ABC
thus
∠A + ∠ B +∠ C = 180° ( Angle sum property of a triangle )
than the third equation becomes
A + B + C = 180 ( third equation)
Now solve the equation
A+B -C =45
and B + C -A = 60
Now subtract B + C -A = 60 from A+B -C =45
we get
(A+B -C) - (B + C -A) = 45-60
2A -2C = -15
Put this value in the equation 2A + 2B - 2C = 90
-15 + 2B = 90
2B = 90 + 15
B = 52.5
now subtracted -A +B +C = 60 from A + B + C =180
A + B + C +A - B - C =180 - 60
2A = 120
A = 60
Put the value of A , B in the equation A + B + C =180
60 + 52.5 + C = 180
C = 180 - 112.5
C = 67.5
Thus ΔABC is an acute angle triangle
therefore
∠A = 60°
∠B = 52.5°
∠C = 67.5°
Hence proved
Write 14/25 29/50 53/100 13/20 and 3/5 in order from greatest to least
Which division expression is equivalent to
The correct answer would be A. 13/3 Divided by -5/6
The total answer would be negative 5 1/5
because you do 4x3+1=13 over the denominator that is already there so 13/3 then you do KCF a.k.a keep change and flip you keep 13/3 change the division sign into multiplication sign then you flip the -5/6 to -6/5 then multiply straight across and reduce this is the way my teacher taught me how to remember - to positive kind of things:
when a negative thing or bad thing happens to a good person is that good or bad in this case thats bad because if you think about it if a bad thing happend to someone you care about that would be bad. then that same idea goes for each pattern another example could be a good thing (+) happens to a good person (+) it is good (+)
(+) (+)=+
(-) (-)=+
(+) (-)= -
(-) (+)= -
Hope this helps. Have a good day! :)
If 5 friends wanted to share 1.25 of a pizza evenly how much each person get
0.25 = [tex]\frac{1}{4}[/tex]
1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
there are 5 quarters thus each person woud get one quarter
Negative one fourths times negative six elevenths
You multiply fractions simply by multiplying numerators and denominators with each other:
[tex] -\dfrac{1}{4} \times \left(-\dfrac{6}{11}\right) = \dfrac{1 \times 6}{4 \times 11} = \dfrac{6}{44} = \dfrac{3}{22} [/tex]
4. Find mQ
A.) 76
B.) 104
C.) 66
D.) 114
See the attached picture for the solution:
Answer:
76=R
R=76
180-76-38=66
Step-by-step explanation:
please help asap 30 pts
[tex]4w-2(1-w)=-38\qquad|\text{use distributive property}\\\\4w+(-2)(1)+(-2)(-w)=-38\\\\4w-2+2w=-38\qquad|\text{add 2 to both sides}\\\\4w+2w=-36\\\\6w=-36\qquad|\text{divide both sides by 6}\\\\\boxed{w=-6}[/tex]
Answer: d. w = -6When you multiply 2.54 by 0.2 how may digits are behind the decimal in the answer
11 = − 3k − 22 − 8k
K equals what?
11 = -3k - 22 - 8k
11 = -11k - 22 added like terms (-3k and -8k)
+22 +22
33 = -11k
[tex]\frac{33}{-11} = \frac{-11k}{-11}[/tex]
-3 = k
Answer: k = -3
What is 3.56×10 to the -5th power in standard form
The ratio of the number of chickens to the number of ducks on a farm was 3 : 8. There were 40 more ducks than chickens. When half the chickens and some of the ducks were sold, the ratio of the number of chickens to the number of ducks became 3 : 4. How many ducks were sold?
Answer:
The number of ducks were sold be 48
Step-by-step explanation:
Let the number of chicken be 3x and the number of ducks on a farm be 8x.
From the given conditions, it is states that there were 40 more ducks than chicken, i.e
8x+40=3x
or [tex]8x-3x=40[/tex]
or 5x=40
Simplify:
[tex]x=8[/tex]
Then, the number of chicken be [tex]3x=3\cdot 8=24[/tex]
and the number of ducks be, [tex]8x=8\cdot 8=64[/tex].
Since it is given that half the chicken and some of the ducks were sold ; then the ratio of the number of chicken to the number of ducks became 3:4
Let the number of ducks that were sold be y.
now by above condition, we have
[tex]\frac{12}{64-y}= \frac{3}{4}[/tex]
then,
[tex]12\cdot 4= 3\cdot (64-y)[/tex]
Simplify:
[tex]48=192-3y[/tex] or
[tex]3y=192-48[/tex] or
[tex]3y=144[/tex]
On simplify we get,
y=48.
Therefore, the number of ducks were sold be, 48.
Final answer:
By setting up simultaneous equations based on the given ratios and the additional information, we can determine that initially there were 120 chickens and 160 ducks. After selling half the chickens and some ducks, 80 ducks were sold to maintain the new ratio of 3:4.
Explanation:
Let's denote the number of chickens as c and the number of ducks as d. According to the problem, the initial ratio of chickens to ducks is 3:8, so we can write the relation as 3d = 8c. Since there are 40 more ducks than chickens, we have the equation d = c + 40.
Now we'll solve these two equations simultaneously. Multiplying both sides of the first equation by c to eliminate fractions, we get 3d = 8c, or 3(c + 40) = 8c. Simplifying this, we find that c = 120 (the number of chickens) and d = 160 (the number of ducks).
After selling half of the chickens and some ducks, the ratio becomes 3:4. The new number of chickens is 120/2 = 60. Let's call the new number of ducks d'. Then, we have 3d' = 4x60. Solving for d', we get d' = 80. Since initially there were 160 ducks and now there are 80, 80 ducks were sold.
Please help with one question. A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 10x - 0.025x² The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?
The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.
For maximum r, r'(x) = 0
It becomes: r'(x) = [tex]10-0.025\times2x=0[/tex]
= [tex]10-0.5x=0[/tex]
[tex]x=\frac{10}{0.05}[/tex]
x= 200
Hence, r(200) = [tex]10\times200-0.025\times200^{2}[/tex]
Solving it we get,
r(200) = 1000
Hence, maximum revenue is $1000.
Triangle KLM was dilated according to the rule DO,0.75 (x,y). What is true about the image △K'L'M'? Check all that apply. DO, 0.75 (x,y) = (0.75x, 0.75y) LM is parallel to L'M'. KM is shorter than K'M'. The vertices of the image are closer to the origin than those of the pre-image. The distance from M' to the origin is exactly half the distance from M to the origin.
Answer: The correct statements are 0.75 (x,y) = (0.75x, 0.75y) , LM is parallel to L'M' and "the vertices of the image are closer to the origin than those of the preimage".
Explanation:
It is given that the triangle ABC was dilated according to the rule DO,0.75 (x,y)
DO, 0.75(x,y) represents the rule of dilation. Where both x- and y-coordinates are multiplied by 0.75 the dilation is about the origin has a scale factor of 0.75. The notation for this dilation would be,
[tex](x,y)\rightarrow (0.75x,0.75y)[/tex]
Therefore, the first statement is true.
Since both x- and y-coordinates are multiplied by 0.75, therefore the sides of image and preimage are parallel but the sides of image are 0.75th of the side of preimage.
Therefore, the second statement "LM is parallel to L'M'" is true but the third and fifth statement is false.
The scale factor is 0.75 which is less than 1, so the vertices of the image are closer to the origin than those of the pre-image.
Therefore, the forth statement "The vertices of the image are closer to the origin than those of the pre-image" is true.
Answer: 124
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER
The manager of the café is creating his menu for the next week. He doesn't want to include items that did not sell as well as the others. Based on this line graph, which item should the manager consider leaving off the menu?
A. Spinach Salad (red line)
B. Turkey Sandwich (green line)
C. Vegetable Soup (blue line)
D. Chicken Souffle (yellow line)
Ok so logically it would be the blue which is consistently low and unlike the others doesn't get any spikes of interst so BLUE.
Paula has 6 video games. Myles has 1 more video game than paula. What can you use to find how many video games in all?
Consider the sequence
2/1, 3/8, 4/27, 5/64, 6/125...
Assuming this pattern continues, find the 11th term.
The 11th term in the given sequence is 11/59049 according to the expressed pattern which is n/(3^(n-1)).
Explanation:The given sequence is a mathematical sequence, where each term appears to be the result of dividing an ascending integer numerator by the ascending powers of 3 in the denominator. Essentially, the pattern of the sequence can be expressed as n/(3^(n-1)) for the nth term. By this pattern, the 11th term in this sequence would fall into the pattern by substituting n = 11, which gives us 11/(3^10).
To simplify the term, you can leave it as 11/59049 as it’s the simplest form.
Therefore, the 11th term of this sequence is 11/59049.
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Which of the binomials below is a factor of this trinomial x^2+13x+42
My Sister Needs Help Lol
On a farm, the farmer decides to give pizza to her 15 ducks as a special treat. She orders 3 pizzas, and the total price is $23.46. What is the unit price of each pizza?
Beth has 250 comic books in her collection. She begins to sell 20 of them each week. Martin has 80 comic books in his collection. He begins buying 15 new comic book each weeks
And Whats the question here?!?!
A blueprint for a house has a scale of 1:35(in:in). A wall in the blueprint is 3inches. What is the length( in feet) of the actual wall
8.75 feet
trust me i got it right on my test ;;
Answer:
1: 3; Enlargement
2: 1/2
3. 8.75 feet
4: 560 millimeters
Step-by-step explanation:
I got 4/4. Hope this helps!
Answer please, will award Brainiest!
The answer for x is 9. Hope this helps. See work below.
i think the answer is 9 hope this helps
The sum of a number and twenty is greater than four times the number decreased by one solve the inequality
After translating the statement into an inequality and simplifying, we find that the solution to 'The sum of a number and twenty is greater than four times the number decreased by one' lies in the set of numbers that is less than 7.
Explanation:The question asks us to solve an inequality. Let's take the given statement: 'The sum of a number and twenty is greater than four times the number decreased by one'. We can translate that into an inequality as follows: x + 20 > 4x - 1, where x stands for the unknown number.
Now, let's simplify the inequality: we subtract x from both sides to get 20 > 3x - 1, and then add 1 to both sides, yielding 21 > 3x. Lastly, divide each side by 3 for the final inequality x < 7.
So the solution to the inequality means any number less than 7, when added to 20, is greater than four times the number minus one.
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Given the graph of a line y=−x. Write an equation of a line which is parallel and goes through the point (−8,2).
y = -x - 6
the equation of a line in ' slope- intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
y = - x is in this form with m = - 1 and c = 0
note that parallel lines have equal slopes thus
the partial equation is y = - x + c
To find c substitute ( - 8, 2 ) into the partial equation
2 = 8 + c ⇒ c = 2 - 8 = - 6
y = - x - 6 ← is the equation of the parallel line
What are the outliers in this data set 78, 87, 81, 16, 64, 100, 88, 10, 87, 110, 108, 149
Answer: 10 & 16
Step-by-step explanation:
Rosa's test scores are 78, 92, 88, and 89. What must she score on her next test to have an average of 90? A) 95 B) 97 C) 99 D) 103
Answer: D
Step-by-step explanation:
Let x represent the score on her next test
[tex]\frac{78 + 92 + 88 + 89 + x}{5} = 90[/tex]
[tex](5)\frac{78 + 92 + 88 + 89 + x}{5} = (5)90[/tex]
78 + 92 + 88 + 89 + x = 5(90)
347 + x = 450
-347 -347
x = 103
In the figure below, segment AC is congruent to segment AB:
Which statement is used to prove that angle ABD is congruent to angle ACD?
Triangle ACD is similar to triangle ABD.
Triangle ACD is congruent to triangle ABD.
Segment AD is congruent to segment AC.
Segment AD is congruent to segment DC.
Answer:
B.Triangle ACD is congruent to triangle ABD
Step-by-step-explanation:
We are given that AC is congruent to segment AB
We have to prove that angle ABD is congruent to angle ACD
When triangle ACD is congruent to triangle ABD
Then ,Angle ACD is congruent to angle ABD
Angle ADC is congruent to angle ADB
Angle CAD is congruent to angle DAB
Segment CD congruent to segment BD
Because when two triangles are congruent then sides and length of a triangle congruent to its corresponding sides and angles of other triangle .
Therefore,Triangle ACD is congruent to triangle triangle ABD is used to prove that angle ABD is congruent to angle ACD.
Hence, option B is true.