Answer:
The two factors of the first number are -4 and 9.
Step-by-step explanation:
We're given:
Two numbers have a product of -36The same two numbers have a sum of 5Let the two numbers be a and b:
[tex]ab=-36[/tex][tex]a+b=5[/tex]Solving for bIsolate a in the second equation and solve for b:
[tex]a+b=5\\a=5-b[/tex]
[tex](5-b)b=-36\\5b-b^2=-36[/tex]
Arrange in [tex]ax^2+bx+c=0[/tex] format:
[tex]-b^2+5b+36=0[/tex]
Divide both sides by -1:
[tex]b^2-5b-36=0[/tex]
Factor:
[tex]b^2+4b-9b-36=0\\b(b+4)-9(b-4)=0\\(b-9)(b+4)=0[/tex]
Solve for b using the zero product property:
[tex]b=-4,9[/tex]
Solve for aSubstitute b back into the second equation to solve for a:
[tex]a+b=5[/tex]
First, let b = -4:
[tex]a-4=5\\a=9[/tex]
Let b = 9:
[tex]a+9=5\\a=-4[/tex]
These are confusing can anyone help with this?
Answer:
3. B
Step-by-step explanation:
Teresa’s age is 5 years more than twice Ben’s age.
If Ben is x years old, the expression gives the sum of Ben’s and Teresa’s ages.
If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is years.
Answer:
The first answer is 2x + 5
The second answer is 19
Identify the coordinates of Point B after it is reflected across the y-axis.
(4, -3)
(4, 3)
(-4, 3)
(-4, -3)
Answer:
(-4,3)
Step-by-step explanation:
the coordinate (4,-3) is just at the 4th quadrant in which the value of x is positive and the value of y is negative
the quadrant (4,3) is on the first quadrant and the value expressed with the letter A
the coordinate (-4,-3) is a coordinate on the quadrant in which both values are negative
1/15 divided by 5/7 please
Answer:
7/75
Explantion:
To get the answer as a fraction you must first have a common denominator
so . .
[tex]\frac{1}{15}[/tex][tex]\frac{5}{7}[/tex]105 is a common denominator
So . .
Multiply 5/7 by 15
Multiply 1/15 7
This comes out as
[tex]\frac{7}{105}[/tex][tex]\frac{75}{105}[/tex]Divide = 7/75
find the value of y and x
Answer:
in my wisdom i think x=60 and y=60
The quotient of c and 6
Answer:
c/6 or c divided by 6
Step-by-step explanation:
Suppose that the average bill for the drive through of 24 customers at Burger Palace is $14.30. It is known that the population standard deviation is σ=2.30. Estimate the true mean bill for a customer at Burger Palace with 95% confidence.
The standard deviation is a measure of a collection of values' variance or dispersion. The true mean bill for a customer at Burger Palace with 95% confidence is $13.38.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Given that the Sample mean ([tex]\overline x[/tex]) is $14.30, the Sample size(n) is 24 customers, the Standard deviation(σ) is 2.30, while for a 95% confidence interval the Z-score is 1.960. Therefore, the true mean can be written as,
[tex]Z = \dfrac{\overline x- \mu}{\frac{\sigma}{\sqrt n}}\\\\\\1.960 = \dfrac{14.30-\mu}{\frac{2.30}{\sqrt{24}}}\\\\\\1.960 = \dfrac{14.3-\mu}{0.47}[/tex]
μ = 13.3788 ≈ 13.38
Hence, the true mean bill for a customer at Burger Palace with 95% confidence is $13.38.
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6x-3=5x-5 multi step equation
Answer:
x = -2
Step-by-step explanation:
Given
6x - 3 = 5x - 5Solving
Add 3 to each side.
6x - 3 + 3 = 5x - 5 + 36x = 5x - 2Subtract 5x from each side.
6x - 5x = 5x - 2 - 5xx = -2find two integers whose sum 2and product is _3
Answer:
The two integers should be 3 and 1
Determine m
117 degrees; supplementary
27 degrees; supplementary
27 degrees; complementary
None of these
117 degrees; complementary
Answer:
27 degress; complementary
Step-by-step explanation:
complementary is when is adds up to 90 and you need 27 more degrees to make it 90
Answer:27 degrees
Step-by-step explanation:
just need points
x+5= 3(x-4) + 5
What is the answer
Step-by-step explanation:
x + 5 = 3x -12 + 5
x + 5 = 3x - 7
Subtract 5 from both sides....
x + 5-5 = 3x -7 - 5
x = 3x - 12
Change the sign ...
12 = 3x - x
12 = 2x
12/2 = x
x = 6
hence 6 is the answer.......
[tex]\large\textsf{\textbf{Answer\::}}[/tex]
x=6
[tex]\large\textsf{\textbf{Calculations\::}}[/tex]
First , use the Distributive Property :
x+5=3(x-4)+5
x+5=3x-12+5
x+5=3x-7
subtract 3x on both sides :
x-3x+5=-7
-2x+5=-7
Subtract 5 on both sides :
-2x=-7-5
-2x=-12
divide by -2 on both sides :
x=6
We've found the value of x : x = 6 .
[tex]\footnotesize\text{hope\:helpful~}[/tex]
Please solve with explanation (high points)
8.1. If x is the distance from P to the flagpole and h is the height of the flagpole, then
tan(53°) = h/x
tan(28°) = h/(x + 20)
Solve for the first equation for h in terms of x :
h = x tan(53°)
Substitute this into the second equation and solve for x :
tan(28°) = x tan(53°) / (x + 20)
(x + 20) tan(28°) = x tan(53°)
x tan(28°) + 20 tan(28°) = x tan(53°)
x (tan(28°) - tan(53°)) = -20 tan(28°)
x = 20 tan(28°) / (tan(53°) - tan(28°))
x ≈ 13.4 m
8.2. By the law of cosines,
BD² = 7² + 11² - 2 • 7 • 11 cos(110°)
⇒ BD = √(170 - 154 cos(110°))
⇒ BD ≈ 14.9 cm
and
BC² = BD² + 16² - 2 • BD • 16 cos(40°)
⇒ BC = √(426 - 154 cos(110°) - 32 cos(40°) √(170 - 154 cos(110°)))
⇒ BC ≈ 10.6 cm
Now use Heron's formula. If S is the semiperimeter of ∆ABD and S' is the semiperimeter of ∆BCD, i.e.
S = (AB + BD + AD)/2 ≈ 16.5 cm
S' = (BC + CD + BD)/2 ≈ 20.7 cm
then
area ∆ABD = √(S (S - AB) (S - BD) (S - AD)) ≈ 36.2 cm²
and
area ∆BCD = √(S' (S' - BC) (S' - CD) (S' - BD)) ≈ 76.7 cm²
so that the total area of ABCD is approximately 112.9 cm².
Verify the Identity!!
Answer:
Check the proof below
Step-by-step explanation:
try to verify from RHS to LHS
(Tan a + tan b) / (tan a - tan b)
= (sin a / cos a + sin b /cos b) / ( sin a/ cos a - sin b/ cos b)
= (sin a cos b + cos a sin b)/ (sin a cos b - cos a sin b)
= sin (a+b) / sin (a-b)
Fyi
sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
1) How did you decide which prints she could order with out cutting off part of the picture? Explain using properties of similar figures. Be sure to explain in sentences. Make sure you include the following vocabulary words: similar figures, scale factor, dilation, ratio, side lengths, measurement
The ability to be able to decide which prints she could order is to look at the environment especially the empty space and then visualize what is missing and what best to fit in.
What are Similar Figures?Similar figures are known to be figures that are said to be of the same shape. They are known to have the same exact size, or one may be bigger than the other.
Note that when two shapes are similar, it is said that their corresponding angles are often same. The angles are also known to be the same because the shape is still of the same shape and as such one can be able to tell from the way or order of the similarity based on the way that the angles match up and also in the scenario above.
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-2a(-5d-4c) answer this
Answer:
10ad+8ac
Step-by-step explanation:
I know trust me.
Can someone help me with this please ignore the question on the bottom
Answers:
DiameterSemicirclePoint of TangencyInternal Common TangentMajor ArcRadiusCenter of a CircleExternal Common TangentSecantChordMinor Arc===========================================================
Explanations:
The diameter is a segment that goes through the center of a circle. Both endpoints are on the circle's edge. The diameter is twice the radius.Arc EGF forms a half circle, better known as a semicircle. The measure of angle EBF is 180 degrees, which is half of a full 360 rotation.Point G is a point of tangency. It's the point of tangency of the two circles, and also the point of tangency for any particular circle and the tangent HJ.Line HJ is the internal common tangent. It is tangent to both circles. We consider it internal since it crosses over the line segment that would connect the centers A and B. Notice that the external tangent KF does not cross the segment that would connect A and B.Arc CDK is a major arc of circle A. By definition, a major arc is anything larger than a semicircle. In other words, if its measure is over 180 degrees, then we have a major arc. A minor arc is anything smaller than 180.Segment BF is a radius of circle B. It is half the diameter EF. If you know the radius, then double it to get the diameter. The radius is from the center of the circle to any point on the circle's edge.Point A is the center of circle A. We label the circle names based on their center.As mentioned earlier, line KF is a external common tangent to the circles. It is tangent to both circles, and it is external in the sense it doesn't cross over line segment AB (you'll have to draw in line segment AB to see that it doesn't cross).Line CD is a secant line. A secant line crosses a circle at exactly two different points. In contrast, a tangent line only touches a circle at exactly one point.Segment GK is a chord. It's basically the segment version of a secant line. A chord is any segment where the endpoints are on the circle's edge. The diameter is a special type of chord.Arc CK is a minor arc. We start at C and travel the shortest distance along the circle to arrive at point K. This is less than a semicircle, so it's why we go with minor arc instead of major. The measure is less than 180 degrees.Find the measure of the missing angle.
Answer:
Step-by-step explanation:
a = 180 - 112
= 68 degrees (adjacent angles)
The sum of two consecutive odd integers is 680 what are the integers
Answer:
let the first number and second number be x+1 and x+3 respectively
Since the beginning of the month a local reservoir has been losing water at a constant rate. On the 10th of the month, the reservoir held 300million gallons of water and on the 18th it held only 262 million gallons. A. Write an equation that will give the amount of water in the reservoir at any time B. Hov, much water was in the reservoir on the 14th of the month? C. When will the reservoir get empty?
Total amount in the reservoir = amount of water in the 10th month - (rate of decline x number of months from the 10th month)
Rate of decline = (300 262) / (18 - 10) = 4.75
y = 300 million = 4.75x
Where x is the time of the month.
What will be the quantity of water in the reservoir on the 14th of the month?Total amount in the reservoir = amount of water in the 10th month - (rate of decline x number of months from the 10th month)
300 million - (4.75 x 4) = 281 million
When will the reservoir be empty?
0 = 300 - (4.75x)
x = 300 / 4.75
x = 63.16 days
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A smoothie recipe calls for 2 and 1 4th cups of frozen mango if the recipe serves two how many cups of frozen mango is needed to serve one
Answer:
The required number of cups of frozen mango is 1.125.
Step-by-step explanation: Given that a smoothie recipe calls for cups of frozen mango and the recipe serves two.
We are to find the number of cups of frozen mango that is needed to serve one.
We will be using the UNITARY method to solve the problem.
We have
The number of cups of frozen mango that needs to serve two is
Therefore, the number of frozen mango that needs to serve one is given by
Thus, the required number of cups of frozen mango is 1.125.
Step-by-step explanation:
NO LINKS!!! Please assist me with the problem 5a
Answer:
g(x) = -x +1
Step-by-step explanation:
The transformation that reflects f(x) across the y-axis is replacement of x with -x.
__
For f(x) = x +1, replacement of x with -x will perform the desired transformation:
g(x) = f(-x) = (-x) +1
g(x) = -x +1
Reflection across y axis rule
(x,y)=(-x,y)so x turns negative
hence f(x) turns f(-x)new one is
g(x)=f(-x)
g(x)=-x+1Describe the net for a square pyramid with a base with edges of 6 inches and slant height of 4 inches. Calculate the surface area of the square pyramid. Enter your answer and explanation.
The square pyramid with a base with edges of 6 inches and slant height of 4 inches have a surface area of 84 in².
The net of the square pyramid have a base of 6 inches and the height of each triangle is 4 inches.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The square pyramid with a base with edges of 6 inches and slant height of 4 inches. Hence:
Surface area = (6 * 6) + 2(6 * 4) = 84 in²
The net of the square pyramid have a base of 6 inches and the height of each triangle is 4 inches.
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If log(16)=s, what is the value of 2/3 log(6400) - 1/3 log(1600) in terms of s?
The value of [tex]\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)[/tex] in terms of s will be
[tex]\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)[/tex]
What is Logrithm?A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Here we have the expression:-
[tex]\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)[/tex]
So in terms of s the expression will become:-
[tex]\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)[/tex]
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For Thursday's English class, 4 students are assigned to give presentations. How many different ways can the teacher order the student presentations?
Answer:
24 ways
Step-by-step explanation:
By the Fundamental Counting Principle,
Number of permutations = 4 ⋅ 3 ⋅ 2 ⋅ 1
= 4!
= 24
There are 24 different ways the teacher can order the student presentations.
Please help!
Will give brainliest to whoever explains.
Answer:
First we need to determine what cos is asking for. Using Soh Cah Toa we can tell that we are using adjacent (a) and hypotenuse (h). The leg that is adjacent to Q is equal to 10 while the hypotenuse is equal to 21.
[tex]cos(Q)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(Q) = \frac{10}{21}[/tex]
After getting to this part, we have to take the inverse of cos in order to cancel the cos on the left and leave Q by itself.
[tex]cos^{-1}(cos(Q))=cos^{-1}(\frac{10}{21})[/tex]
[tex]Q = 61.56\ degrees[/tex]
In the end we are left with that our angle Q is equal to 61.56 degrees.
Hope this helps! Let me know if you have any questions
What is the value of x?
Answer:
9
Step-by-step explanation:
x is 9 assuming they are identical triangles.
A computer can sort x objects in t seconds, as modeled by the function
below:
t=0.003.x² +0.001.x
How long, in seconds, will it take the computer to sort 12 objects?
Round your answer to the nearest hundredth of a second.
We are given that, a computer can sort x objects in t seconds, and the below relations is satisfied for each x and t
t = 0.003 x² + 0.001 xFor 12 objects, we can substitute x = 12
⇒ t = (3/1000) (12)² + (1/1000) 12
⇒ t = (12/1000) (3 × 12 + 1)
⇒ t = (12×37/1000)
⇒ t = 444/1000
⇒ t = 0.444
⇒ t ≈ 0.40 seconds (2 dp)
I need help solve this
Answer:
36
Step-by-step explanation:
Area of a triangle = A = hb x b
A = 12 x 7 = 84 2
84/2 = 42
rectangle area = l x w
2 x 3 = 6
42 - 6
36
What is an element NOT found in creative writing?
A. conflict
B. plot
C. works cited
D. description
Answer:
it should be c
Step-by-step explanation:
can you guys help me please :(
Ok then im doing the 3rd one:
Area of a parallelogram =b.h
[tex]11 \frac{3}{4} \times 8 \frac{1}{3} \\ = 11.75 \times 8.33 \\ = 97.8775 \\ = \boxed {97.9}[/tex]