Answer:
x=4 or x= -2
Step-by-step explanation:
(x-1)(x-1)
x(x-1)-1(x-1)
x^2-x-x+1
x^2-2x+1=9
x^2-2x+1-9=0
x^2-2x-8=0
p= -8
s= -2
1------ -8
2------ -4
x^2+2x-4x-8=0
x(x+2)-4(x+2)
(x+2)(x-4)=0
x+2=0
x-4=0
x= -2
or
x=4
An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.
Answer:
71° and 71°.⠀
Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
⠀
So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.⠀
We know that,
The sum of all angles of a triangle is 180°⠀
So, According to the question :
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]
⠀
Therefore,
The measure of the two other angles of the isosceles triangle are 71° and 71°.The middle school will lose some of its funding if 50 or more students move away in any year. The principal claims he only loses about 30 students a year. Do the values in the table support his claim? Explain.
Change 7 kilometres to metres ?
In each diagram shown below, solve for the length of side CD using the information given. Show the trig ratio you use and your algebra to find your final answer. Round all answers to the nearest tenth
Applying the trigonometry ratios, we have:
a. CD = 63.6
b. CD = 33.8
c. CD = 16.1
d. CD = 15.9
What are the Trigonometry Ratios?The trigonometry ratios are used to find a length or angle in any right triangle. They are:
SOH, which is sin ∅ = opp/hypCAH, which is cos ∅ = adj/hypTOA, which is tan ∅ = opp/adja. ∅ = 32°
hyp = 75
adj = CD
Apply CAH:
cos 32 = CD/75
CD = cos 32 × 75
CD = 63.6
b. ∅ = 56°
opp = 28
hyp = CD
Apply SOH:
sin 56 = 28/CD
CD = 28/sin 56
CD = 33.8
c. ∅ = 43°
opp = 15
adj = CD
Apply TOA:
tan 43 = 15/CD
CD = 15/tan 43
CD = 16.1
d. ∅ = 27°
hyp = 35
opp = CD
Apply SOH:
sin 27 = CD/35
CD = sin 27 × 35
CD = 15.9
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Write two different expressions that
represent the quantity x decreased
by 30%.
Answer:
Step-by-step explanation:
x - 30 = 14 - 3x
4x = 44
x = 11
Let's call the unknown number x
Now let's decrease it by 30, that is x-30
Now let's write out "14 decreased by three times the number", that is 14 - 3x
The problem says these are the same, that is x - 30 = 14 - 3x
We now want to isolate, or solve for, x
Move the x to one side of the equation by adding 3x to both sides
3x + x -30 = 14 - 3x + 3x
4x -30 = 14
Now move the 30 to the right hand side by adding 30 to both sides
4x - 30 + 30 = 14 + 30
4x = 44
Now all we have to do to get x is divide both sides by 4
4x/4 = 44/4
x = 11
Number 5? Pre Cal- A small airplane is cruising at an airspeed of 235 kph heading in a direction of 45° (measured from the positive z-axis). The wind is blowing at 60kph in a direction of 120°. Find the resulting direction and groundspeed of the airplane to the nearest whole number.
Answer:
c
Step-by-step explanation:
c
In a basketball game, you made 4 baskets out of 12 attempts. Your teammate made 3 baskets out of 8 attemps
Answer:
4/12 and 3/8
Step-by-step explanation:
Given f(x) = 3x2 + kx – 7, and the remainder when f (x) is divided by x – 4 is
81, then what is the value of k?
Answer:
-243
Step-by-step explanation:
{3׳ykx-7 incluye
how do I multiply 6ab (xa+ya^6 +8)
Answer:
6xba^2 + 6yba^7 + 48ab
Step-by-step explanation:
To do this, you have to multiply 6ab by each of the inside terms,
So you can write it out like this
6ab (xa + ya^6 + 8)
6ab(xa) + 6ab(ya^6) + 6ab(8)
Then you can simplify:
6xba^2 + 6yba^7 + 48ab
(When you multiply the same variable by itself, you turn it into an exponent)
For example x * x = x^2
Or x^4 * x^3 = x^7
I need help on this question
0.007 kg
Step-by-step explanation:[tex]1000\ grams=1\ kg\\ 7\ grams=0.007\ kg\\ Check\ conversion[/tex]
I hope this helps you
:)
The number of students taking algebra increased 20% in one year. If
60 students are taking algebra this year, how many took algebra last
year?
Answer: 50 students
Step-by-step explanation:
You know that the number of students last year plus 20% of that number equals the number of students this year, which can be written as: x + 0.2x = 60 →
1.2x = 60 → x = 50 students :)
Answer: 50 students
Step-by-step explanation:
x + .2x = 60
1.2x = 60
x = 60/1.2
x = 50
the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle. pls help. solve using applications of quadratics
Answer:
[tex]2m[/tex]
Step-by-step explanation:
Alrighty let's do this.
We know that formula for the Area of a triangle is:
[tex]A = \frac{1}{2}bh[/tex]
They give us the area as [tex]6m^2[/tex], so let's include it in the equation.
[tex]6 = \frac{1}{2}bh[/tex]
Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that [tex]h = b-4[/tex]
So replace [tex]h[/tex] in the equation with [tex]b-4[/tex].
You will now get:
[tex]6 = \frac{1}{2}b(b-4)[/tex]
Now we can work towards solving. Let's get simplifying.
[tex]12 = b(b-4)\\12 = b^2 - 4b\\[/tex]
bring everything to one side so we can make a quadratic and factor:
[tex]0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2[/tex]
We get that [tex]b=6[/tex].
Since we need the height of the triangle we'll need to call back on what h is. We found earlier that [tex]h = b - 4[/tex], so to find h, we just sub in our b value into that.
[tex]h = (6) - 4 = 2[/tex]
We find that [tex]h=2[/tex]
Hi ..
I really need help on this one
Answer:
LCM of 3 and 2 is 6
so, firstly we had to make the denominator same:-
[tex] \frac{2(2a + 1) + 3(3a - 1)} {6} [/tex]
[tex] \frac{4a + 2 + 9a - 3}{6} [/tex]
[tex] \frac{13a - 1}{6} [/tex]
Step-by-step explanation:
hope this helps you!!!
XxITSCHOCOLOVERxX
The simplified equation of [tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex] is [tex]\frac{13a-1}{6}[/tex]
How to simplify an equation?[tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex]
[tex]\frac{2a+1}{3}+\frac{3a-1}{2} = \frac{2(2a+1)+3(3a-1)}{6}[/tex]
open the bracket in the numerator
Therefore,
[tex]\frac{2(2a+1)+3(3a-1)}{6}=\frac{4a+2 + 9a-3}{6}[/tex]
combine like terms in the numerator
[tex]\frac{4a+2 + 9a-3}{6}=\frac{4a+9a+2-3}{6}[/tex]
Hence,
[tex]\frac{4a+9a+2-3}{6}=\frac{13a-1}{6}[/tex]
Therefore, the final equation is as follows
[tex]\frac{2a+1}{3}+\frac{3a-1}{2}=\frac{13a-1}{6}[/tex]
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24. generalize what are the attributes of fractions
that are equivalent to 100%
Answer:
when a fraction equals 100% it means it has the same numbers for its numerator and denominator such as 4/4 or 18/18
Step-by-step explanation:
When it has the same numbers for its numerator and denominator it will be 100%
1) Find the slope of the line
2) Find the slope between the two points.
help please, thank you
Answer:
Slope formula;
y2(second y coordinate) - y1(first y coordinate)
____________________________________
x2(second x coordinate) - x1(first x coordinate)
Plug in values:
2 - 1 1
_______ = ________, your slope is -1/14.
-17 - (-3) -14
Solve the equation 4 ( c - 3 ) = 8
Answer:
c=5
Step-by-step explanation:
4(c-3)=8 Distribute
4c-12=8 Add 12 to both sides
4c=20 Divide by 4 on both sides
c=5
Answer:
c = 5Step-by-step explanation:
METHOD 1:
4(c - 3) = 8 |divide both sides by 4
4(c - 3)/4 = 8/4
c - 3 = 2 |add 3 to both sides
c - 3 + 3 = 2 + 3
c = 5
METHOD 2:
4(c - 3) = 8 |use the distributive property: a(b - c) = ab - ac
4 · c - 4 · 3 = 8
4c - 12 = 8 |add 12 to both sides
4c - 12 + 12 = 8 + 12
4c = 20 |divide both sides by 4
4c/4 = 20/4
c = 5
solve systems by substitutions
y=x + 10
y= -6x-18
x + 10 = - 6x - 18
7x = - 28
x = - 4
and y = - 4 + 10 = - 6
This one is hard! try your best please.
A box contains 9 identical glass spheres that are used to make snow globes. The spheres are tightly packed, as shown below.
Answer:
1. 301.6 [tex]in^{3}[/tex]
2. 576 [tex]in^{3}[/tex]
3. 274.41 [tex]in^{3}[/tex]
Step-by-step explanation:
We know that the diameter of one of the spheres must be 4 in, because the length of the box is 12 in and there are 3 spheres along each side, and [tex]\frac{12}{3} =4[/tex]. That means that the radius of a sphere is 2 in. Put 2 into the formula for the volume of a sphere, and then multiply your solution by 9, to get the total volume.
Then, you can find the volume of the box, because you know its dimentions are 12x12x4.
Subtract your answer for part 1 from your answer for part 2, and you have the solution to part 3. Hope this helps!! :-)
These cones are similar. find the surface
area of the smaller cone. round to the
nearest tenth.
2 cm
3 cm
surface area = [? ] cm2
surface area = 75 cm?
Answer:
33.3 is your answer
Step-by-step explanation:
The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Two cones A₁ and A₂ are similar.
The radius of A₁ = 2 cm
radius of A₂ = 3 cm
The surface area of A₁ = ? cm²
surface area of A₂ = 75 cm²
Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.
Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,
(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)
We can use this relationship to solve for the surface area of A₁:
(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)
Substituting the given values, we get:
(surface area of A₁) = (2/3)² × 75
(surface area of A₁) = 4/9 × 75
(surface area of A₁) ≈ 33.3 cm²
Therefore, (surface area of A₁) ≈ 33.3 cm²
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help please this assignment is due in a few minutes
Answer:
C. 200 hours
Step-by-step explanation:
According to the given Question ,
Speed of Aeroplane is 400miles/hourIt means that the aeroplane covers 400 miles in 60 minutes.
and it is asked for 30 minutes , so
We know that 30 minutes is equal to 0.5 hours
By the formula ,
Distance = Speed × Time
putting the values given , we get
= 400×0.5
Distance = 200 miles
Given f(x)=x^3+9x+k, and x-1 is a factor of f(x), then what is the value of k?
Answer:
r:
The function is
The remainder when f(x) is divided by x−2 is 23.
To find:The value of k.
Solution:
According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).
It is given that, the remainder when f(x) is divided by x−2 is 23. By using remainder theorem, we get
Put x=2, to find the value of f(2).Therefore, the value of k is 8.
Step-by-step explanation:
40 students go to a sport centre in buses. a bus can hold 14 students. find the number of buses needed
Answer:
The answer is 3 buses
Step-by-step explanation:
40 divided by 14 is 2.85714285714 buses well you cant have 3/4 of a bus so you round it up to 3 buses
Find the value of X
4.5
8.9
6.5
X
13
b
11
can someone answer
Jamal would like to purchase a pair of shoes for $80.00. At the store he can spin the spinner below to receive a discount
John paid $75 for a pair of shoe that cost $100 at a discount of 25 percent.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the shoe cost $100, he spins the spinner and gets a discount of 25%, hence:
Money paid = 100 - 25% of 100
Money paid = 100 - 25 = $75
John paid $75 for a pair of shoe that cost $100 at a discount of 25 percent.
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Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.
How many more cookies will Jessica have than Martha?
If x represents the number of cookies Jessica started with, complete the statements below.
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.
Answer:
Part A: [tex]x^2-30x+224\geq 0[/tex]
Part B: Jessica has at least 2 cookies more than Martha
Step-by-step explanation:
Since there are 2 question-
Let,
How many more cookies will Jessica have than Martha?If x represents the number of cookies Jessica started with, complete the statements below. Be Part A:
Let,
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0 Jessica has at least _ cookies more than Martha.
Be Part B:
Hint:
J=Jessica
30-J=Martha
(J-6)*((30-J)-6)<=80
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve:
Starting with Part A: Find the inequality that describes the relationship between the number of cookies each one of them has
Let,
"x" be the number of cookies when Jessica started
"30-x" be the number of cookies when Martha started
Given us that:
Each of them ate 6 cookies from their bag
Therefore,
Cookie left in each bag are:
(x-6) which is - Jessica
30 - x - 6 = (24 - x) - Martha
Solution - (x-6)(24-x)
The product of the number of cookies left in each bag is not more than 80.
Thus,
[tex](x-6)(24-x\leq 80[/tex]
[tex]24x-x^2-144+6x\leq 80[/tex]
[tex]-x^2+30x-144-80\leq 0[/tex]
[tex]-x^2+30x-244\leq 0[/tex]
[tex]\mathrm{Multiply\;by\;-1\;both\;sides}[/tex]
[tex]x^2-30x+224\leq 0[/tex]
Hence, Answer = [tex]x^2-30x+224\leq 0[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve:
Part B: Solve the quadratic equation:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:14\le \:x\le \:16\:\\ \:\mathrm{Interval\:Notation:}&\:\left[14,\:16\right]\end{bmatrix}[/tex]
[tex]\left(x-14\right)\left(x-16\right)\le \:0[/tex]
[tex]14\le \:x\le \:16[/tex]
The solution is x=16 cookies
Thus, (30-x)=30-16=14 cookies
Now we know that;
The number of cookies when Jessica started was 16 cookies
The number of cookies when Martha started was 14 cookies
So,
The number of cookies left in each bag is equal to
Jessica:
16-6=10 cookies
Martha:
14-6=8 cookies
10 > 8
As a result, Jessica has at least 2 cookies more than Martha.
Fill in blank for:
The inequality that describes the relationship between the number of cookies each one of them has is x^2 - __30__ x +224 >= 0.
Jessica has at least __2__ cookies more than Martha.
~Lenvy~
Solve the equation and enter the value of x below.
-3x-9=-27
x=
Answer:
6
Step-by-step explanation:
-3x=-27+9
-3x=-18
x=-18/-3
x=6
Answer:
[tex]\displaystyle 6 = x[/tex]
Step-by-step explanation:
[tex]\displaystyle -3x - 9 = -27 \hookrightarrow \frac{-3x}{-3} = \frac{-18}{-3} \\ \\ x = 6[/tex]
I am joyous to assist you at any time.
Finish the steps below to write a quadratic function for the parabola shown. use the vertex form, f(x) = a(x – h)2 k, and substitute in the values for h and k. f(x) = a(x – 5)2 3 use another point and substitute in values for x and f(x). solve for a. 5 = a(6 – 5)2 3 write the function, using the values for h, k, and a. the function is f(x) = (x – )2 .
The vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
Substitute the values for h and k in the above vertex form.
[tex]f(x) = a(x -5)^2+ 3[/tex]
Use another point and substitute in values for x and f(x). Solve for a.
[tex]5 = a(6 - 5)^2 +3\\5-3=a(1)\\a=2[/tex]
Rewrite the function, using the values for h, k, and a. The function is
[tex]f(x) = 2(x -5)^2+ 3[/tex]
Hence, the vertex form of the parabola after finishing the steps and putting the values for h, k, and a, is [2(x -5)²+ 3]
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Answer: 1st slot: 2 | 2nd slot: 5 | 3rd slot: 3 | correct on edge 2023!
What is the measure of arc c e d? 106° 108° 148° 212°.
Answer:
Can you please give us figure of following ?
Answer:
its the last one 212°
212°
212°
212°
212°
212°
Step-by-step explanation:
212°
Angel had $21 to spend on two notebooks. After buying them he had $13 left. How much did each note book cost?
Answer:
each notebook would cost $4
Step-by-step explanation:
21-13=8. 8/2=4
Which expressions are equivalent to Tan(< g
Answer:
Can u post a picture so I can see what your talking about!?