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We need to translate "five times the sum of a number and -23" into an algebraic expression.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Can you see the word "sum" there? It tells us to add.So in this case we should add a number (let it be x) and -23:
[tex]\star~\large\pmb{x+-23}[/tex]
Which is the same thing as
[tex]\star~\large\pmb{x-23}[/tex]
Now we multiply this little expression by 5, which gives us
[tex]\star~\large\pmb{5(x-23)}[/tex]
The parentheses around the expression indicate that we multiply 5 by the entire expression, and not just one term.
Hope it helps you out! :D
Ask in comments if any queries arise.
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What is the volume, in cubic meters, if the prism below?
=================================================================
Explanation:
Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.
The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.
Multiply this floor area with the height of the room (22 m) to get the volume of the room.
volume = (floor area)*(height) = 84*22 = 1848 cubic meters
Draw the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D'
What are the two points?
The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.
From the graph:
The two points are (-4, -2) and (4, 5)
The line equation passing through two points:
[y - 5] = (5+2)/(4+4)[x - 4]
y - 5 = 7/8[x - 4]
8y - 40 = 7x - 28
8y = 7x + 12
Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.
Learn more about the geometric transformation here:
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HELP PLEASE! THIS IS DUE SOON! HELP ME! QUESTION BELOW!
Answer:
A) x = 113°
Explanation:
Given three sides: 6.4 cm, 5.8 cm, 10.2 cm
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert/put variables:
[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]
[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]
[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]
[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]
[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex] = 113.36° ≈ 113° (rounded to nearest degree)
Graph f(x)=2^x what is the answer?
Graph is in attached image.
Simplyfy 56 64 I want to simplify
Answer:
56/64 simplified is 0.875 or 7/8 as a fraction
ILL GIVE BRAINLYEST TO RIGHT ANSWER! The graph of a line has a positive slope if if is:
A. increasing/going up
B. horizontal
C. decreasing/going down
D. vertical
Answer: The correct answer is A.
Step-by-step explanation: A line with a positive slope always increases and goes up.
X^2-4x+6=0 solve by completing square
Complete the square:
x² - 4x + 6 = 0
x² - 4x = -6
x² - 4x + 4 = -6 + 4
(x - 2)² = -2
But the left side is positive for any real number x, so there are no real solutions.
If you're solving over the complex numbers, we can go on to say
x - 2 = ± √(-2)
x - 2 = ± 2i
x = 2 ± 2i
where i = √(-1).
Write this number in standard notation.
Answer:
12345678910
Step-by-step explanation:
TANQR
The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]
The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]
What is scientific notation?It is the way of writing a large number between 1 to 10 with a power of 10.
We have,
7,250,000
To write this number in standard notation, we can use powers of 10.
We start by counting the number of digits to the left of the decimal point.
In this case, there are 7 digits to the left of the decimal point.
We can then express this number in scientific notation as:
[tex]7.25 \times 10^6[/tex]
This means that we have 7.25 times 10 raised to the power of 6.
Now,
0.000045
To write this number in standard notation, we can again use powers of 10. We start by counting the number of digits to the right of the decimal point. In this case, there are 5 digits to the right of the decimal point.
We can then express this number in scientific notation as:
[tex]4.5 \times 10^{-5}[/tex]
This means that we have 4.5 times 10 raised to the power of -5.
Thus,
The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]
The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]
Learn more about scientific notation here:
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The complete question.
Write this number in standard notation.
7,250,000
0.000045
AD are tangent to OC. Find the value of x.
NEED HELP WITH THIS QUESTION QUICK!!!
Answer:
x=5
Step-by-step explanation:
The two lines are the same length
2x+7 = 5x-8
15 = 3x
x = 5
WHAT ARE THE ANSWERS TO 1,2,3,4 SOMEONE HELP!!!!!
Answer:
1) Ans; C .
2) Ans; D.
3) Ans; A.
4) Ans; C.
Answer and EXplanatrion please
Answer:
whats nine + 10
Step-by-step explanation:
21
pencil is .10
pen is .90
Step-by-step explanation:
x = pencil y = pen
3x + y = 1.20
7x + 2y = 2.50
try make x or y cancelable
-2 times (3x + y = 1.20) = -6x - 2y = - 2.40
7x + 2y = 2.50
-6x - 2y = - 2.40
x = .10
plug .10 back into one of the equations
3(.10) + y = 1.20
.30 + y = 1.20
y = .90
The diameter of a circle is 5 meters. What is the circumference?
Answer:
15.71 m
Step-by-step explanation:
C = πd
d= diameter
C = π (3.14) * 5
= about 15.71 m
A. 15.71 m
Answer:[tex]5\pi[/tex]
Step-by-step explanation:The circumference is pi times the diameter. If you want a proof you can find it online with a quick search. This applied here means that since the diameter is 5, the circumference is 5*pi or rather 5pi.
3/y-3=12/y+3, what is y?
Answer:
i am not sure about your question but if it is 3 divided by y-3 =12 divide by y+3 you can use this
Step-by-step explanation:
3÷y-3=12÷y+3
cross multiply
12(y-3)=3(y+3)............brackets off
12y-36=3y+9..............group the same
12y-3y=9+36
9y=45.......duved by 9 both sides
y=5
A sample of 4 different calculators is randomly selected from a group
containing 46 that are defective and 26 that have no defects. What is the
probability that all four of the calculators selected are defective? Round to four
decimal places.
A) 0.1021 B) 0.1586 C) 0.1666 D) 10.9154
[tex]\displaystyle\\|\Omega|=\binom{72}{4}=\dfrac{72!}{4!68!}=\dfrac{69\cdot70\cdot71\cdot72}{2\cdot3\cdot4}=1028790\\|A|=\binom{46}{4}=\dfrac{46!}{4!42!}=\dfrac{43\cdot44\cdot45\cdot46}{2\cdot3\cdot4}=163185\\\\P(A)=\dfrac{163185}{1028790}=\dfrac{473}{2982}\approx0.1586[/tex]
Which graph represents the following system of inequalities?
y>2x-5
y<-3x
give an answer with graph
The graph of the two given system of inequalities y > 2x - 5
y < -3x is; Attached below
How to graph Inequalities?We are given two inequalities;
y > 2x - 5
y < -3x
The graph that represents the 2 inequalities has been attached and from the graph, we see that;
The slope of the dotted line is negativeThe x- intercept of the dotted line is the point (0,0)The y- intercept of the dotted line is the point (0,0)The solution of the system of inequalities is the shaded pink area between the two dotted lines.
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If f(x) = 2x² +2 and g(x)=x²-1, find (f- g)(x).
Directions: Solve the following by multiplying by the inverse of the fractional coefficient. 1. \frac{2}{5} t = 20 2. \frac{7}{8} p = 56 3. \frac{5}{6} x = 30 4. \frac{1}{2} x = 20 5. \frac{3}{5} s = 60 6. \frac{1}{3} t = 3 7. \frac{3}{4} x = 9 8. \frac{11}{12} x = 11 9. \frac{8}{10} t = 80 10. \frac{p}{3} = 9 11. \frac{n}{5} = 30 12. \frac{6a}{7} = 36 13. \frac{1}{2} t + 3 = 28 14. \frac{1}{6} r = 12 15. \frac{11}{12} b = 32
The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.
How to interpret the fraction?Suppose the fraction is proper (the numerator is smaller than the denominator).
Let it be
[tex]\dfrac{a}{b}[/tex]
Then, we can interpret it as:
a parts out of b parts of a thing.
[tex]1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50[/tex]
[tex]2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64[/tex]
[tex]3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36[/tex]
[tex]4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40[/tex]
[tex]5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100[/tex]
[tex]6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9[/tex]
[tex]7. \frac{3}{4} x = 9\\\\x = 12[/tex]
[tex]8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12[/tex]
[tex]9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100[/tex]
[tex]10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27[/tex]
[tex]11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150[/tex]
[tex]12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42[/tex]
[tex]13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50[/tex]
[tex]14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72[/tex]
[tex]15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33[/tex]
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G(F(x)) = 7√√x+1
A. F(x)=√x and G(x) = 7
B. F(x)= x and G(x) = √√7
C. F(x) = 7x and G(x)=√x+1
D. F(x)=√x+1 and G(x) = 7x
Answer:
D)
Step-by-step explanation:
[tex]\sf f(x) = \sqrt{x+1}\\\\\\g(x) = 7x\\\\ g(f(x)) = g(\sqrt{x+1}) = 7*\sqrt{x+1}[/tex]
One block is needed to make an up-down-up staircase with one step up and one step down.
Four blocks are need to build and up-down-up staircase with 2 steps up and 2 steps down.
Complete parts (a) and (b) below.
***
a. How many blocks are needed to build an up-down-up staircase with 5 steps up and 5 steps down?
25 blocks are needed to build an up-down-up staircase with 5 steps up and 5 steps down.
(Type a whole number.)
b. How many blocks are needed to build an up-down-up staircase with n steps up and n steps down?
blocks are needed to build an up-down-up staircase with n steps up and n steps down.
Answer:
n² blocks are needed to build a staircase with n steps.
Step-by-step explanation:
solve 2(r+6) =(6+1/3r)
Answer:
r = - 18/5
I hope this helps! ^^
( This problem has 13 steps, so it would take a lot of time to type them in ^^)
Write the solution to -9×+4<40??
Answer:
Simplifying
-9 + 4 = 40
Combine like terms: -9 + 4 = -5
-5 = 40
Solving
-5 = 40
Couldn't find a variable to solve for.
This equation is a the left and right sides are not equal, therefore there is no solution.
Hope This Helped
Help me out, please!
Answer:
a = 63
b = 117
c = 63
Step-by-step explanation:
The sum of interior angles in a triangle is = 180
so the measure of a:
85 + 32 + a = 180 add like terms
117 + a = 180 subtract 117 from both sides
a = 63
a and be are supplementary angles so their sum is equal to 180
180 - 63 = 117 is the b's value
since a and c are on a pair of parallel lines, their value must be equal therefore the value of c is also 63
Write a story that could represent this math problem. 2/6 times 3/4
A baseball "diamond" is actually a square with side lengths of 90 feet. In a game, a runner tries to steal second base. How far must the catcher throw from home plate to second base in order to get the runner out?
Answer:
about 127.28 feet
Step-by-step explanation:
The length of the hypotenuse of a right triangle with a base and a height of 90 feet each.
root (90)^2 + (90)^2
Solve for x. Write both solutions, separated by a
comma.
6x² + 5x - 6= 0
Answer:
[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]6x^2+5x-6=0[/tex]
First, factor the left side of the given equation.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=6\cdot-6=-36[/tex]
[tex]\implies b=5[/tex]
So the two numbers are: 9 and -4
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 6x^2+9x-4x-6=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 3x(2x+3)-2(2x+3)=0[/tex]
Factor out the common term [tex](2x+3)[/tex]:
[tex]\implies (3x-2)(2x+3)=0[/tex]
To solve for x:
[tex]\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}[/tex]
Therefore:
[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]
The methods of solving quadratic equations
There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.
[1] using the quadratic formula
When the equation is in the form of ax² + bx + c = 0.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Read more about the quadratic formula here:
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[2] factoring
Read more about how to solve with factoring here:
https://brainly.com/question/25829061
[3] completing the square
To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c
Read more about completing the square here:
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12.simplify the following expression
21q + 5/2(3/2) + 4q -5
Answer:
i think the answer is 25q - 5 / 4
Solve |2x + 1| = 10?
[tex]|2x+1|=10\\2x+1=10 \vee 2x+1=-10\\2x=9 \vee 2x=-11\\x=4.5 \vee x=-5.5[/tex]
Answer:
[tex]x= \dfrac 92~~\textbf{or}~~x = -\dfrac{11}2\\\\[/tex]
Step-by-step explanation:
[tex]\underline {\textbf{Absolute value rule: }}\\\\\textbf{If}~ |a| = b~ \textbf{then} ~a =b~ \textbf{or}~ a =-b \\\\\underline{\textbf{Solution;}}\\\\\textbf{Given that,}\\\\~~~~~~~|2x+1| = 10\\\\\implies 2x +1 = 10~~~~~~\textbf{or} ~~~~~~~~~~~2x+1 = -10\\\\\implies 2x = 10-1~~~~~~\textbf{or}~~~~~~~~~~~2x = -10-1\\\\\implies 2x = 9~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~2x = -11\\\\\implies x= \dfrac 92~~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~x = -\dfrac{11}2\\\\[/tex]
what is the mean of 7,5,6,5,4,4,,8,6,6,7,4,5,5,6,6
Answer:
5.6 is the mean
Step-by-step explanation:
add up everything and then divide it over how many numbers are in the set to find the mean.
give brainliest, please!
hope this helps :)
find the quantity if v=5i-7j and w=3i+2j ||v||-||w||
[tex]\begin{cases} v=5i-7j\\\\ w=3i+2j \end{cases}\qquad \begin{cases} < \stackrel{a}{5}~~,~~\stackrel{b}{-7} > \\\\ < \stackrel{a}{3}~~,~~\stackrel{b}{2} > \end{cases}\qquad \qquad \stackrel{magnitude}{\sqrt{a^2 + b^2}} \\\\[-0.35em] ~\dotfill\\\\ ||v||~~ - ~~||w||\implies \sqrt{5^2+(-7)^2}~~ - ~~\sqrt{3^2 + 2^2}\implies \sqrt{74}-\sqrt{13} ~~ \approx ~~ 5[/tex]