The linear equation with a slope of 1 that passes through (3, 5) is:
y = x + 2.
How to get the linear equation?
The general linear equation is given by:
y = a*x + b
Where b is the y-intercept and a is the slope.
Here we know that the slope is 1, so we have:
y = x + b
And we also know that the line passes through (3, 5), then we must have that:
5 = 3 + b
We can solve that for b:
b = 5 - 3 = 2
So the linear equation is:
y = x + 2.
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a regular number cube is rolled. What is the probability that a 3 will not be rolled?
•1/6
•1/2
•4/5
•5/6
Answer:
5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
probability(event) = (number of desired outcomes)/(total number of outcomes)
The total number of outcomes is 6 since there are 6 different sides on the cube.
The number of desired outcomes is 6 minus 1 for rolling a 3, so it is 5.
p(not 3) = 5/6
Given the equation y= 3x + 8, what would be the value of y be when x = 3?
A. 17
B. 14
C. 1
D. 15
Answer:
[tex]y = 17[/tex]
Step-by-step explanation:
We were given the equation
[tex]y = 3x + 8[/tex]
and we were told that x = 3, therefore y would be
[tex]y = 3x + 8 \\ y = 3(3) + 8 \\ y = 9 + 8 \\ y = 17[/tex]
Bell sells pies each week at the farmers market. She spends $65 on materials and charges $10 per pie. She hopes to make a profit of at least $15 per hour. What constraints might bell want to set?
Answer:
43.33
Step-by-step explanation:
You will start out by putting 65 in time 10 divide by 15 and that will give you your answer
Answer:
43.33
Step-by-step explanation:
You will start out by putting 65 in time 10 divide by 15 and that will give you your answer
30. What is the length of XPY in terms of pie ?
675 m
225 m
457 m
15 m
Answer:
circumference = 2 x PI x r= 2 x 3.14 x 30 = 60 PIthe area from x to y = 90 degrees so XPY would be 360 - 90 = 270 degrees or 3/4 of a full circleso XPY = 60 x 3/4 = 45 PI meters
3 What is the solution to ža>-16? o a O a>-21 a 21 O a
Answer: The answer is the first option: [tex]a > -21\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] × [tex]a > -16[/tex]
[tex]\frac{3}{4}a\cdot \frac{4}{3} > -16\cdot \frac{4}{3}[/tex]
[tex]\frac{3}{4}\cdot \frac{4}{3}a > -16\cdot \frac{4}{3}[/tex]
[tex]a > -16\cdot \frac{4}{3}[/tex]
[tex]a > \frac{-16\cdot 4}{3}[/tex]
[tex]a > \frac{-64}{3}[/tex]
Determine which expressions represent purely real numbers and which expressions represent non-real complex numbers. -i^2+i^3 7-5i √ 6 0+9i √(-5)^2 -12 2 -7i^2
purely real number
non-real complex number
Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
What are Purely real numbers and Non-real complex numbers?Purely real numbers are in the form of a+0i, while the Non-real complex numbers are in the form of a+bi.
The given expressions can be simplified in the following manner,
[tex]-i^2+i^3 = -(\sqrt{-1})^2+(\sqrt{-1} \times \sqrt{-1} \times \sqrt{-1}) = 1 -i[/tex] 7-5i [tex]\sqrt{-6} = \sqrt{-1 \times 6} = \sqrt{-1} \times \sqrt{6} = 0+ i\sqrt{6}[/tex]i⁶ = (i²)³ = (-1)³ = -1 = -1 +0i0+9i [tex](\sqrt{-5})^2 = (\sqrt{-1 \times 5})^2 = -1 \times 5 = -5+0i[/tex] -12 = -12+0i[tex]2 -7i^2 = 2-7(-1) = 2+7 = 9+0i[/tex]Purely real numbers (a+0i)
-1 +0i-5+0i-12+0i9+0iNon-real complex number (0+bi)
1-i7-5i0+i√60+9iLearn more about Purely real numbers and Non-real complex numbers:
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Answer:
Step-by-step explanation:
go to BYJU's learning app and get to expert answer
pls help me with this 10 ponits
Answer:
I believe it is B
Step-by-step explanation:
What is the distance between the following points?
Answer:
7.615773105864
Step-by-step explanation:
[tex]\text{let A and B be the points of coordinates} \ A\left( 3,-9\right) \text{and} \ B\left( 6,-2\right)[/tex]
[tex]AB=\sqrt{\left( 6-3\right)^{2} +\left( -2-(-9)\right)^{2} }[/tex]
[tex]=\sqrt{\left( 3\right)^{2} +\left( 7\right)^{2} }[/tex]
[tex]=\sqrt{58} =7.615773105864[/tex]
Flying with the wind, a plane flew 1,200 mi in 4 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind.
Answer:
Rate of plane = 250 mph
Rate of wind = 50 mph
Step-by-step explanation:
Let the speed of the plane in calm air be x mph& speed of the wind be y mphSpeed of plane with wind = (x + y) mphSpeed of plane against wind = (x - y) mphFormula relating speed, time and distance is given as: speed*time = distanceAccording to the first condition: (x+y)*4 = 1200-> x + y = 300 (1)According to the second condition: (x-y)*6= 1200-> x - y = 200 (2)Adding equations (1) & (2), we find:2x = 500-> x = 250 (Dividing 500 by 2)-> y = 50 (Plugging x = 250 in eq 1)Rate of plane = 250 mphRate of wind = 50 mphStanley walks a round-trip of 1.75 miles to work every day. How many miles will he walk in 5.5 days
A. 9.625 miles
B. 96.25 miles
C. 962.5 miles
D. 9625 miles
Multiply miles per day by number of days
5.5 x 1.75 = 9.625
answer: A. 9.625 miles
Write the equation of the line that passes through the point
(1,−5) and with the slope of −3. Write the in slope-intercept form.
Answer:
y = -3x -2
Step-by-step explanation:
Hi there!!
We're given that a line has a slope of -3 and it contains the point (1, -5)
We want to write the equation of this line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
As we are already given the slope, we can immediately plug it into the equation.
Replace m with -3 in y=mx+b.
y = -3x + b
Now we need to find b
As the equation passes through the point (1, -5), we can use its values to help solve for b.
Substitute 1 as x and -5 as y:
-5 = -3(1) + b
Multiply
-5 = -3 + b
Add 3 to both sides
-2 = b
Substitute -2 as b into the equation
y = -3x - 2
Hope this helps!
Topic: finding the equation of a line
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A triangular pane of glass has a height of 36 inches and an area of 396 square inches. What is the length of the base of the pane?
The length of the base of the pane is blank
inches.
Answer:
see the attachment photo!
comparing -4 to -5 integers
what they have in common is that there both Intergers but What's different is that there -1 off
How much would you
have to
deposit today to have an
accumulated amount of
$20,000 in 20 years
if yearly
interest is 4.75% compounded
continuously?
Dusan says that ∆XYZ ~ ∆TUV because two pairs of angles are congruent. Is he correct? If not, why? Yes, he is correct. No, because two pairs of congruent angles cannot prove similarity. No, because the third angle measure cannot be determined. No, because there is only one set of congruent angles.
Answer:
No, because there is only one set of congruent angles.
Step-by-step explanation:
I took the instruction, and this was the right answer!
Answer:
D
Step-by-step explanation:
Choose ALL the numbers that round down when rounding to the nearest hundred! Is it!: 47,035, 3,140, 76,654, 1,298, 607,882, 8,560?
Answer:
The answer is:
the first one
second one
:D
Step-by-step explanation:
in this case, any number in the tens place less than five will make the number round down
Find the standard deviation of the data, 12, 19, 9.
Answer:
4.19
Step-by-step explanation:
Find the mean:
[tex]\text{Mean}=\frac{12+19+9}{3}=\frac{40}{3}[/tex]
Find the standard deviation:
[tex]\text{Standard Deviation}=\sqrt{\frac{(12-\frac{40}{3})^2+(19-\frac{40}{3})^2+(9-\frac{40}{3})^2}{3}}=\sqrt{\frac{158}{9}}\approx4.19[/tex]
Which is the graph of Y=Vx-5-1
Answer:
^^
Step-by-step explanation:
Answer:
Slope: 1
y-intercept: (0, -6)
Let f(x) = x² + 4x - 6 and g(x) = x + 2, find (f • g)(x).
Answer:
(f.g)(x) = (f×g)(x)
= (x² + 4x - 6) × ( x + 2)
= x^3 + 2x^2 + 4x^2 + 8x - 6x - 12
= x^3 + 6x^2 + 2x -12
Suppose Marco draws a cross-section of the cube shown below and the result is a triangle. Describe how Marco could have sliced the cube to produce a triangular cross-section.
If JK = 20, KL = x + 9, and JL = 6x + 9, what is KL?
[tex]\underset{\leftarrow ~~ 6x+9 ~~ \to }{J\stackrel{20}{\rule[0.35em]{15em}{0.25pt}} K\stackrel{x + 9}{\rule[0.35em]{10em}{0.25pt}} L} \\\\\\ \stackrel{JL}{6x+9}~~ = ~~\stackrel{JK}{20}+(\stackrel{KL}{x+9})\implies 6x+9=29+x\implies 5x+9=29 \\\\\\ 5x=20\implies x=\cfrac{20}{5}\implies x=4\hspace{5em}\boxed{\underset{KL}{\stackrel{(4)~~ + ~~9}{13}}}[/tex]
According to the fundamental theorem of algebra, which polynomial function has exactly 6 roots? f (x) = 5 x superscript 4 baseline 10 x squared 2 f (x) = 5 x superscript 5 baseline 3 x superscript 4 baseline 12 x cubed 7 x squared minus 2 x 15 f (x) = 6 x superscript 5 baseline x cubed minus 4 x squared x minus 5 f (x) = 7 x superscript 6 baseline 3 x cubed 12
The polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12. Then the correct option is D.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
According to the fundamental theorem of algebra.
The polynomial function has only exactly 6 roots.
The roots are the value of the variables in the polynomial at which the value of the polynomial is zero.
If the degree of the variable is n then the number of the roots will be n or less than n.
If the number of the roots are 6, then the degree of the variable will be 6 in the polynomial.
Then the polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12.
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Given that 5 cos (x+8.5)° - 1 = 0
0° ≤x≤ 90, calculate correct to the nearest degree, the value of x.
Answer:
x = 70
Step-by-step explanation:
To solve for x, use inverse operations to undo the operations performed on x.
__
5cos(x +8.5)° -1 = 0 . . . . given
5cos(x +8.5)° = 1 . . . . . . add 1
cos(x +8.5)° = 1/5 . . . . . divide by 5
x° +8.5° = arccos(1/5) . . . . take the inverse cosine
x° = arccos(1/5) -8.5° ≈ 70° . . . . evaluate the expression
The value of x is 70.
XYZ is a right triangle If XY = 8, what is XZ?
Answer:
square root of 64 minus yz square
What is the volume?
2 mm
4 mm
2 mm
Answer:
16mm
Step-by-step explanation:
that's because volume is lwh ( length X width X height)
Complete the Proof Statements Reasons 1. ABCD is a given AC BD 2. AD BC 3. 4. AABC=ABAD 5 ZDAB=LCBA 6. 7. ABCD is a rectangle 1. 2. 3. 4. 5. 6. 7. Congruent supp. angles are right angles 8. Given: ABCD is a parallelogram AC = BD Prove: ABCD is a rectangle SSS Triangle Congruence Theorem mZDAB = 90° m/CBA = 90° Reflexive Property of Congruence ZDAB and ZCBA are supplementary Definition of Rectangle O B CPCTC If the quad is a both pairs of opposite sides are congruent Consecutive angles in a are supplementary AB = AB
1) ABCD is a parallelogram, [tex]\overline{AC} \cong \overline{BD}[/tex] (given)
2) [tex]\overline{AD} \cong \overline{BC}[/tex] (if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent)
3) [tex]\overline{AB} \cong \overline{AB}[/tex] (reflexive property of congruence)
4) [tex]\triangle ABC \cong \triangle BAD[/tex] (SSS Triangle Congruence Theorem)
5) [tex]\angle DAB \cong \angle CBA[/tex] (CPCTC)
6) [tex]\angle DAB[/tex] and [tex]\angle CBA[/tex] are supplementary (consecutive angles in a parallelogram are supplementary)
7) [tex]m\angle DAB=90^{\circ}, m\angle CBA=90^{\circ}[/tex] (congruent supplementary angles are right angles)
8) [tex]ABCD[/tex] is a rectangle (definition of rectangle)
All the missing statements with the respective reasons are given below.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Statement 1.
ABCD is a parallelogram,
AC ≅ BD
Reason: Given.
Statement 2.
AD ≅ BC
Reason: if the quadrilateral is a parallelogram, both pairs of opposite sides are congruent.
Statement 3. AB ≅ AB
Reason: reflexive property of congruence.
Statement 4. ΔABC ≅ ΔBAD.
Reason: SSS Triangle Congruence Theorem
Statement 5. ∠DAB ≅ ∠CBA
Reason: CPCTC
Statement 6. ∠DAB and ∠CBA are supplementary
Reason: consecutive angles in a parallelogram are supplementary.
Statement 7. m∠DAB = 90° and m∠CBA = 90°
Reason: congruent supplementary angles are right angles.
Statement 8. ABCD is a rectangle.
Reason: definition of a rectangle.
Therefore, all the required points are given above.
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Find the area of the figure. Round to the nearest hundredth where necessary.
55 mm
32.5 mm
12.5 mm
12.5 mm
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Data and Calculations:Contingency Table
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Answer:
Step-by-step explanation:
6.81
Three trends each have a balance of $5,000 on their credit cards with a 25%APR. They've
decided that they will not make any other purchases on the cards until they pay of the debt
and make varying amounts of monthly paymentes
• Sharon can only make the credit card minimum payment, $150 per month
• Ceollia can set aside $400 per month to pay back her dett
• Alexander can pay $800 per month for his credit card
After 5 months, how much will each person have paid in interest so far and how large will
their remaining balance be? Use the formulas below to calculate their interest and balance
for each month
Hint Credit card interest is typically compounded daily so n=365Time here is in years, so
make sure you use a fraction for your t value. Need to show monthly interest and balance paid monthly for first 5 months on each person.
here i hope this exaple helps but for the time being while i solve it heres this example
if you currently owe $500 on your credit card throughout the month and your current APR is 17.99%, you can calculate your monthly interest rate by dividing the 17.99% by 12, which is approximately 1.49%. Then multiply $500 x 0.0149 for an amount of $7.45 each month.
what is the positive solution of x²-36=5×
Answer:
I'm assuming the x at the end is a variable
9, -4
Step-by-step explanation:
If we replace x with 9, we get 81-36=45 which is 45=45 so 9 is one solution.
If we replace x with -4, we get 16-36=-20 which is -20=20 so -4 is the other solution
So, the solutions are 9 and -4.
Hope this helped you! If there is a mistake in my answer, please tell me and I will correct it as soon as possible.