Answer:
x intercept is 7 y intercept is -3
Step-by-step explanation:
Write equation out and have y=0
[tex] log_{2}(x - 1) - 3 = 0[/tex]
Add 3 to both sides
[tex] log_{2}(x - 1) = 3[/tex]
Using the log to exponet rule
[tex] (log_{b}(x) = y ) \: equal \: b {}^{y} = x[/tex]
Where b and x are real numbers and b cannot equal 1.
Reorder the equation as a exponet
[tex] log_{2}((x + 1) = 3[/tex]
[tex] {2}^{3} = x + 1[/tex]
Simplify
[tex]8 = x + 1[/tex]
Subtract 1 from both sides
[tex]x = 7[/tex]
So the x intercept is 7
To find y intercept plug 0 in as x
[tex] log_{2}(0 + 1) - 3 = y[/tex]
[tex] log_{2}(1) - 3 = y[/tex]
Add 3 to both sides
[tex] log_{2}(1) = y + 3[/tex]
Rewrite in exponet form
[tex] {2}^{y + 3} = 1[/tex]
Using the zero exponet property, anything to the zero power equal 1 so we must find a value that equal out to zero using the exponet so we'll set up the equation
[tex]y + 3 = 0[/tex]
Subtract 3 from both sides and we get
[tex]y = - 3[/tex]
So the x intercept is 7 and the y intercept is -3
A shipping box is in the shape of a rectangular prism. It has a volume of 9,000 in.3, and the dimensions of the base are 20 in. by 30 in. What is the height of the box?
Answer:
A closed box is to be made in the shape of a cuboid of height h (in cm) with a rectangular base that has sides of length x (in cm) and 2x (in cm). Its volume is required to be `1000 cm^3
The height of the shipping box is 15 inches.
What is volume of rectangular prism?The volume of a rectangular prism: length x width x height. The volume is expressed in cubic units.
given:
Volume = 9000 cubic inches
Base dimensions = 20 inches by 30 inches
Now, Volume = Base Area * Height
Height = Volume/Base Area
Height = 9000/(20 * 30)
Height = 15 in
Hence, the height of the shipping box in the shape of a rectangular prism is 15 inches.
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Show work. Will mark branliest
Answer:10
Step-by-step explanation:
12 x 30 to see how many bottles per hour
360 x 8 to see how many it makes in a day
Divide 28,000 by 2,800 to see how many days it would take.
Step-by-step explanation:
first u will find how much bottles in 8 hours so that will be 60/2minutes =30so 30*12ottles=to 360 bottles per hour so 8*360=2,880 so u will do 28,000/2,880 it will be. 10 days of work.
A leisure aircraft is owned by the Broadland Flying Group which has 10 members. The costs of keeping the aircraft comprise maintenance costs (including insurance) and the running cost which is mainly fuel. Average fuel consumption is 9 miles per gallon. If the 10 members of the Group are to share costs equally, write down a formula to enable Gordon the treasurer to calculate the annual cost for each member if the aircraft travels n miles in a year, incurs maintenance costs of £M and fuel costs £3 a gallon.
Answer:
£(M + n/3) / 10
Step-by-step explanation:
Given that :
Number of members = 10
Fuel consumption = 9 miles per gallon
Consumption for n miles = n/9 GALLONS
Cost of fuel = n/ 9 * £3 = 3n / 9 = £n / 3
Maintainace cost = £M
Annual cost per member :
£(M + n/3) / 10
select the correct choice and fill in the box to complete your choice. pls help!!!
find the common factors of the given terms 1. 12x, 36. 2. 2y, 22x. 3. 14pq, 28p^2 q^2
Answer:
answer 1. 12. 2nd is 2. and 3rd is 14pq
hope it helps
Explain how I would use Distributive Property (GCF) to factor the following expression: 4m + 16
Answer:
4(m+4)
Step-by-step explanation:
4m+16
Rewriting
4*m + 4*4
Factor out 4
4(m+4)
I need help on this question
Your family got a coupon for 35% off at Red Robin. Your bill comes to $45.00 before you use the coupon. Sales tax on the discounted meal is calculated at 8%. You then leave a 15% tip based on the original cost of the meal. How much will dinner and tip cost?
Answer: $38.34
Step-by-step explanation:
Original bill total: $45
35% discount: $15.75
subtotal: $29.25
sales tax: 8% of $29.25: $2.34
bill for meal: $29.25 + $2.34 = $31.59
Tip: 15% of original cost of meal: 15% of $45: $6.75
TOTAL COST: $31.59 + $6.75 = $38.34
4d = 30 the answer would be c=7.5 right if not plz correct me if im wrong
Answer:
Correct!
Step-by-step explanation:
You did it the correct mathematical way, where you divide 4 by 30. Some people get confused and multiply 30 and 4, so good job!
Answer:
Step-by-step explanation: 4÷30=7.5 D = 7.5
65°
(х + 72)
i need help with x
Answer:
65x+4680
Step-by-step explanation:
Which multiplication expression does the model represent?
Answer: I think the answer is A. because it's 1/2 of 4 and it takes only one "quarter of the 4" all though it is split in half it still decared as a whole
Step-by-step explanation:
The multiplication expression represent the model is 1/2×4.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
In the given figure, there are 4 equal parts.
One part is divided into two equal parts.
1/2×4
Therefore, the multiplication expression represent the model is 1/2×4.
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Drag each number to the correct location on the table. Classify the real numbers as rational or irrational numbers. Please Help I need the answer today!
Answer:
did you ever figure out what the answer was it was because working on this and don't know what to do
Step-by-step explanation:
Answer:
Rational Numbers: √400 | -5/250 | 5.012121212...
Irrational Numbers: √1000 | ^3√30 | 0.01562138411...
Whats 4x+2=2(x+6) ?
Just want to see your answers
Answer:
x = 5
Step-by-step explanation:
4x + 2 = 2(x + 6)
4x + 2 = 2x + 12 (after you distribute the 2)
add and subtract like terms
4x - 2x = 12 - 2
2x = 10
x = 5
you can double check by substituting the x with 5 in the equation
4 (5) + 2 = 2(5 + 6)
20 + 2 = 2(11)
22 = 22
I can't figure it out.
2x+2y=2
-4x+4y=12
Answer:
how to solve 2x+2y=2 , -4x+4y=12
this is solving equations using substitution .... i have ALOT more but i juss dnt get this stuff
2x + 2y = 2 -4x + 4y = 12
x + y = 1
x = 1 - y
-4x + 4y = 12
-4(1 - y) + 4y = 12
(-4 + 4y) + 4y = 12
-4 + 8y = 12
8y = 16
y = 2
2x + 2y = 2
2x + 2(2) = 2
2x + 4 = 2
2x = -2
x = -1
Check.
-4x + 4y = 12
-4(-1) + 4(2) = 12
4 + 8 = 12
Answer: x = -1 and y = 2
Step-by-step explanation:
Write an equation of the line that passes through (2, 1) and is parallel to the line y=2x+7.
Answer: y=2x-3
Step-by-step explanation:
Factor f(x) = 4x2 + 11x? - 104x + 105 into linear factors given that – 7 is a zero of f(x).
f(x) = 4x + 11x2 - 104x + 105 = |
(Factor completely.)
Answer:
f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5)
Step-by-step explanation:
f(x) = 4x^3 + 11x2 - 104x + 105
has the coefficients {4, 11 -104, 105}. We perform synthetic division using the given -7 as divisor:
-7 / 4 11 -104 105
-28 119 -105
-----------------------------------
4 -17 15 0
Since the remainder is zero (0), we have shown that -7 is a zero of f(x). The coefficients of the quotient (above) are {4, -17, 15}. Let's try factoring the corresponding polynomial again using synthetic division. Start out by using 5 as divisor and determining whether or not the remaindeer is zero:
5 / 4 -17 15
20 15
-------------------------
4 3 30 No, the remainder is 30 and so 5 is not a
root of this quadratic. Try the divisor 3 instead:
3 / 4 -17 15
12 -15
---------------------------
4 -5 0 Yes, the remainder is 0 and so 3 is a root.
Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:
f(x) = 4x + 11x2 - 104x + 105 = (x - 3)(x + 7)(4x - 5). Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.
Need help ASAP
48 ÷ 2 (9 + 3) = ?
Answer:
I think the answer is 288
Step-by-step explanation:
I think this because 48/2=24 and 9+3=12 (parentheses means multiply) 24x12=288
Can someone please help I’ll mark you the brainiest..
Answer:
(-3±√5)/2
This is a quick check so stop asking for help online because it is test related
30 POINTS!!!!! What is the domain for each function below?
Picture included below!
-For the 1st equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and then 3, -3, and 0.
-For the 2nd equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and 0 and 3.
The domain is the set of input values for which the function is real and defined.
Find non negative values for the radicals.
For y = sqrt(3-x) if x is greater than the 3 the value under the square root would be negative which would result in a non real number.
The answer needs to be x <= 3 ( less than or equal to)
For y = sqrt(3x), if x is less than 0, the number under the sqrt root would be negative resulting in a non real number.
The answer is x >= 0 ( greater than or equal to)
What is the value of (Negative one-half)–4?
-16
Negative StartFraction 1 Over 16 EndFraction
StartFraction 1 Over 16 EndFraction
16
Answer: D
The answer is D, 16
Answer:
D is correct.
Step-by-step explanation:
welcome have a good day.
please help me! where are the black dots located?!
the bottom square: -6,-5
the top square: -2,1
(5-8) (1,4) m = -3
find the slope
Answer:
slope is -3
Step-by-step explanation:
m is the slope, this may have been a trick question.
by the points given the slope is 1
Find the value of x
A. 5 square root 2/2
B 5
C 10
D 10 square root 2
Answer:
The answer is C
Step-by-step explanation:
That side with the 5 is equal to 7.071067812.... (irrational number)
To get x you need to use the equation a^2 + b^2 = c^2
A^2 and B^2 will both be the same thing. The red line indicates they are the exact same length.
7.071037812.... ^2 is 50
Now your equation would be 50+50= c^2 (which is the same as x^2)
100= c^2 is simplified by finding the square root of 100.
Your answer is 10 for side X because the square root of 100 is 10.
This problem was solved using the Pythagorean Theorem.
The hypotenuse x of the right triangle is (c) 10
Finding the hypotenuse, x of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Where, we have
Leg a = 5√2
Leg b = 5√2
The hypotenuse of the right triangle can be calculated using the following Pythagoras theorem
h² = a² + b²
Using the above as a guide, we have the following:
x² = (5√2)² + (5√2)²
Evaluate
x² = 100
Take the square roots
x = 10
Hence, the hypotenuse of the right triangle is (c) 10
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What unit should be used to calculating fundraising for field trip
Answer:
the mcps i think
Step-by-step explanation:
Im not sure :/
PLS HELP! i rly need help on this. it’s hard for me.
1: what is the name of that figure??
2: what would be the cross section from a vertical slice of the figure??
Answer:
The 3D solid shown in the image is a hexagonal pyramid. If we made a cross section with a vertical slice (top to bottom), we would have an isosceles triangle.
Useful Extra Knowledge:
However—and this isn't a question here, but just useful knowledge—if we made a cross section with a horizontal slice (left to right or right to left), we would have a regular hexagon. If it were a diagonal cross section, we would have an irregular hexagon.
Step-by-step explanation:
First, what's the difference between a sphere, a cylinder, a pyramid, a cone, and a prism? These are all 3D solids, but in your case, an explanation of what they are may be a good refresher:
A sphere is a 3D solid where every point is equidistant from the center point. Basically, it's a 3D circle. It's completely round.A prism is a 3D solid with straight, parallel sides and a polygonal base.A cylinder is a 3D solid with straight, parallel sides and a circular baseA pyramid is a 3D solid with sides that converge at a common vertex and a polygonal base.A cone is a 3D solid with sides that converge at a common vertex and a circular base.We definitely know this shape can't be a sphere! It's not completely round! Actually, take a closer look: there's no hint of a circle anywhere in the figure. It can't be a cylinder nor a cone.
This means it's either a pyramid or a prism. But, going back to the definitions above, let's redefine the difference between the two: pyramids have only one base and only triangular faces, while prisms have two bases and rectangular faces.
How many bases does this figure have? It has one base. And what shape are its faces? They're all triangles! This means we have to be looking at a pyramid.
So, you may think, that solves it. We're looking at a pyramid.
Sorry, buddy. It's not that easy. We can classify this figure even further. How do we do this? We use its base! And what type of polygon is the base? When we count the sides of the base, we find six sides, which means this shape is a hexagon. So this is a hexagonal pyramid, right?
Actually, there's one more specification we could give this. That hexagon has sides that are all equal to each other. That may not seem special to you, but there's a special term given to polygons who have equal sides and equal inner angles: they are called regular polygons.
That description matches the base of our shape, right? So, now we have the name of the figure: it's a regular hexagonal pyramid.
Now, what about the cross section? This means we're taking a piece of that solid, like cutting into a cake with a knife. Who likes cake here?
I digress. This piece, the cross section of the 3D solid, becomes a 2D shape. Now, the question asks for the shape of a vertical cross section, which means up and down, like the y-axis on the coordinate plane/Cartesian plane.
So, imagine taking a butter knife and slicing right down the middle of that bad boy. If you get the middle point exactly, you'll have two equal halves which would look like triangles with two equal sides: an isosceles triangle.
That's assuming you look straight on at them. If you veered to the side a little, you'd find a scalene triangle (a triangle with no equal sides).
But, should you miss the center a little, you'd get a trapezoid instead, because part of the top would be missing.
But I'm assuming the question is asking about a vertical slice exactly down the middle and viewed straight on. In that case, your answer is an isosceles triangle.
I droned on for a bit, I know. But hopefully this helps you understand the concept better! Have a great day!
Cuánto costará cercar una finca cuadrada de 14 metros de lado a razón de $150 el metro lineal de alambrada
Answer:
$ 2100
Step-by-step explanation:
De la pregunta anterior:
1 metro de cerca de alambre = $ 150
14 metros = x
Cruz multiplicar
x = 14 × $ 150
x = $ 2100
Por lo tanto, costaría $ 2100 por una cerca de 14 metros
Please help me!!!!
3. Compute the product axb in each of the
following cases:
a) a = -7.5
and b=0.25 ;
b) a = -2.5
and b=-18;
c) a = -812
and b=-0.75;
d) a = 4.25 and b= -326.
Answer:
a). -7.5*0.25 = -1.875
b). -2.5*(-18) = 45
c). -812*(-0.75) =609
d). 4.25*(-326) = -1385.5
i rlly need a worded story thingy that equals 2361.
E.g. Jack had 3 apples he a 2 how many apples does he have left ??
That type thing
THANKS xx
Helllllllp
Simplify the expression 43 + 2(3 − 2).
14
16
66
68
Answer:
68
Step-by-step explanation:
Answer:
The answer is 46...i cant find that answer in the choices though
Step-by-step explanation:
In PEMDAS we can see that we have parentheses first so we solve whatever is in the parentheses. which 3-2 = 1....so it should look like this
43 + 2 + 1
Which equals 46
hope this helps. have a good day
Consider the polynomial function q(x) = 3x^4 – 5x^3 – 2x^2 + x – 18.
What is the end behavior of the graph of q?
Answer:
a in the picture
Step-by-step explanation:
The end behaviour of the function is correctly represented by option 1.
What is the end behaviour of a function? What do you mean by domain and range of a function?The end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
For any function y = f(x), Domain is the set of all possible values of [x] for which [y] exists. Range is the set of all values of [y] that exists for the given domain.
Given is the following function polynomial as -
q(x) = 3x⁴ – 5x³ – 2x² + x – 18
The given polynomial is -
q(x) = 3x⁴ – 5x³ – 2x² + x – 18
Graph the function. It can be seen that the domain is limited from -
x = -1.365 to x = 2.351 which is a small value. So, we can predict the end behaviour of the graph as given in option [1].
Hence, the end behaviour of the function is correctly represented by option 1.
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