Answer:
x = 4, -4
Step-by-step explanation:
f(x)= x^2 + 7
f(x) =23
23 = x^2+7
Subtract 7 from each side
23-7 = x^2 +7-7
16 = x^2
Take the square root of each side
±sqrt(16) = sqrt(x^2)
±4 = x
Find the slope of the line that passes through (10, 8) and (1, 4).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
Step-by-step explanation:
4-8 = -4
1-10 = -9
-4/-9 simplifies to 4/9
A paper clip is just over 4 cm long. How many paper clips like this can be made from a straight piece of wire 10 meters long?
Answer:
25 Paper Clips
Step-by-step explanation:
100cm is equal to 1 meter. So to find the answer you would need to take the whole of the centimeter (100) and divide that by the paper clips length (4).
100/4 = 25
So, to form a straight line 10 meters long you would need 25 paper clips each 4cm long.
The number of 2,500 paper clips like the given paper clip can be made from a straight piece of wire that is 10 meters long.
What is multiplication?Multiplication is a type of mathematical operation. The repetition of the same expression types is another aspect of the practice.
For instance, the expression 2 x 3 indicates that 3 has been multiplied by two.
We can start by converting the length of the wire to centimeters since the length of the paper clip is given in centimeters:
10 meters = 10,000 centimeters
To determine the number of paper clips that can be made from the wire, we need to divide the total length of the wire by the length of each paper clip.
Number of paper clips = Total length of wire / Length of each paper clip
Length of each paper clip = 4 cm
Number of paper clips = 10,000 cm / 4 cm
Number of paper clips = 2,500
Therefore, the required number is 2500.
To learn more about multiplication;
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Classify the following triangle. Check all that apply.
Factor the expression below x^2+12+36 A) (x-6)(x-6) B) (x+6)(x+6) C) (x-9)(x-4) D) (x+9)(x+4)
Answer:
Answer B
Step-by-step explanation:
when you simplify it u get x^2+12+36
Find the area of the triangle. Round your answer to the nearest tenth.
A) 101.3 m^2
B) 58.5 m^2
C) 29.3 m^2
D) 50.7 m^2
Answer:
A
Step-by-step explanation:
Which of the following reasons can be used to justify statement #3 in the proof?
A Given
B the vertical angel theorem
C the reflexive property of congruence
D SSS
c because it is accuet.
hope it helps
Option C . The reflexive property of congruence is the correct reason that can justify statement 3 . BD≅BD
What is the reflexive property of congruence?The reflexive property of congruence states that every side, every angle, every line segment and every shape is congruent to itself.
To prove that ΔABD is congruent to ΔCBD where given that
1.Line segment AB ≅ Line segment CB (Given)
2. Then we can write AD ≅CD ; Given : D is the mid point of AC
3. line segment BD ≅ Line segment BD , this is true by reflexive property of congruence which states that every line segment or side is congruent to itself.
BD can be considered as side of both the given triangles
Therefore, the reason that can justify statement 3 is option C.
Also, Learn more about the properties of congruence from the link below:
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How would you describe the curve?
the answer is C, the curve is a one to one function
The sum of the interior angles of a polygon is 8,100. How many sides does the polygon have?
Answer:
explanation below
Step-by-step explanation:
(n - 2) * 180 = 8100
n - 2 = 8100/180
n - 2 = 45
n = 45 + 2
n = 47 sides <---answer
happy to help ya :)
An online retail company tracked total number of purchases monthly. In June 2007 they were 4,500 purchases and in September 2008 there were 5,100. The purchases followed a linear model of the form p = S ( t ) = r t + i where p purchases is in 1000's and t is months where January 2007=0
The linear model for the number of purchases over time is:
p = 0.043t + 3.726
We have,
Let's assign the variable t as the number of months since January 2007, where t = 0 corresponds to January 2007.
Given data:
June 2007: p = 4,500 (in thousands, so p = 4.5)
September 2008: p = 5,100 (in thousands, so p = 5.1)
We can use these data points to set up a system of equations to solve for the slope (r) and the intercept (i) in the linear model p = rt + i.
Using the data points,
4.5 = r(18) + i (June 2007 corresponds to 18 months after January 2007)
5.1 = r(32) + i (September 2008 corresponds to 32 months after January 2007)
Solving this system of equations will give us the values of r and i.
Subtracting the second equation from the first equation:
4.5 - 5.1 = r(18) - r(32)
-0.6 = -14r
r = -0.6 / -14
r = 0.043
Substituting the value of r into one of the equations:
4.5 = 0.043(18) + i
4.5 = 0.774 + i
i = 4.5 - 0.774
i = 3.726
Therefore,
The linear model for the number of purchases over time is:
p = 0.043t + 3.726
Learn more about expressions here:
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The height of the tower is five times the height of the building. If the tower is 52 meter taller than the building.then find the height of the tower
Answer:
Let, height of the Building = x
Height of the Tower = y
Height of the tower is 5 times from height of the building = y = 5x
Height of the tower is 52 meter taller than the building = y-x = 52
put 5x instead of y in the equation y-x=52
5x-x=52
4x=52
x=52/4
x=13 meter
y=5x
y=5(13)
y=65 meter
Julie went shopping at the mall for a new pair of jeans. She saw a pair at Hollister that was marked $50 with a 40% discount. She saw a pair at Abercrombie that was marked $40 with a 20% discount. How much would each pair of jeans cost after the discount?
Answer:
30 and 32
Step-by-step explanation:
Which quantity does this number line represent?
A) less than 5
B) less than 4
C) less than 3
D) less than or equal to 4
What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 52 college students were surveyed and r = 12 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05. (a) What is the level of significance?
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.24
For the alternative hypothesis,
p ≠ 0.24
This is a two tailed test
Considering the population proportion, probability of success, p = 0.24
q = probability of failure = 1 - p
q = 1 - 0.24 = 0.76
Considering the sample,
Sample proportion, P = r/n
Where
r = 12
n = 52
P = 12/52 = 0.23
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.23 - 0.24)/√(0.24 × 0.76)/52 = - 0.17
Recall, population proportion, P = 0.24
The difference between sample proportion and population proportion(p - P) is 0.24 - 0.23 = 0.01
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.24 - 0.01 = 0.23
the p for the right tail is 0.24 + 0.01 = 0.25
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area below the test z score in the left tail 0.43
We would double this area to include the area in the right tail of z = 0.17 Thus
p = 0.43 × 2 = 0.86
The level of significance is 5%
Since alpha, 0.05 < than the p value, 0.86, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, this information does not imply that the color preference of all college students is different (either way) from that of the general population.
Which of the following ribbon has the greatest cost per inch?
You didnt give the sizes of the ribbon so let me help you out. You have to divide the size by total cost, bringing you to the cost per one whatever unit you are using.
The equation of the graphed line is..... x+......y=4 ANSWER FAST PLZZXZZ FILL IN THE BLANKS (DOTED LINE)
Answer:
x+2y=4
Hope this helped
To test the effectiveness of a diet cat food, scientists divided a group of overweight cats into a control and treatment group. The cats in the control group ate their regular food. The cats in the treatment group received a measured portion of diet cat food twice a day. After two months, the cats in the treatment group had lost an average of 1.2 lb, and the cats in the control group had gained an average of 0.1 lb. State the Subjects:
Answer:
Step-by-step explanation:
The subject in a statistical research work usually refer to the participants involved in the experiment which is usually a quantitative research.
The subjects in this study are all the overweight cats including those in the control and treatment groups.
Find the areas of the sectors formed by ∠DFE. Round your answers to the nearest hundredth.
Answer:
Area of the sector in red = 177.87 cm²
Area of the sector in blue = 437. cm²
Step-by-step explanation:
Area of the sector = [tex]\frac{\theta}{360}(\pi )(r)^2[/tex]
Area of the sector shaded in blue = [tex]\frac{256}{360}(\pi )(14)^2[/tex]
= 437.87 cm²
Central angle formed by sector shaded in red = 360 - 256 = 104°
Area of the sector shaded in red = [tex]\frac{104}{360}(\pi )(14)^2[/tex]
= 177.884
≈ 177.88 cm²
Therefore, area of the sector shaded in red = 177.87 cm² and area of the sector in blue = 437.88 cm²
Choco pies are cookies made from chocolate (c), sugar (s), and flour (. Chocolate costs $5 per pound, sugar costs
$3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as
sugar
Calvin wants to invest $12,000 in deposits. For tax purposes, he wants his total interest to be $600. He wants to put
$1000 more in a 2-year deposit than in a l-year deposit and invest the rest in a 3-year deposit. How much money
should he invest in each deposit?
Number of Years
Rate
2.0%
5.09
6.0%
1-year: $2200, 2-year: $3200, 3-year: $6600
1-year: $4000, 2-year: S5000, 3-year: $3000
1-year: S3200, 2-year: $4200, 3-year: $4600
1-year: $1000, 2-year: S2000, 3-year: $9000
Question :
justinapace7446
Yesterday
Mathematics
High School
+5 pts
Choco pies are cookies made from chocolate (c), sugar (s), and flour (. Chocolate costs $5 per pound, sugar costs
$3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as
sugar
Calvin wants to invest $12,000 in deposits. For tax purposes, he wants his total interest to be $600. He wants to put
$1000 more in a 2-year deposit than in a l-year deposit and invest the rest in a 3-year deposit. How much money
should he invest in each deposit?
Number of Years
Rate
2.0%
5.0%
6.0%
Answer:
1-year: $2200, 2-year: $3200, 3-year: $6600
Step-by-step explanation:
Assume y = Amount invested for 1 year.
y + 1000 = investment amount for 2 years
12000 - (y + y + 1000 ) = amount invested for 3 years
11000 - 2y = amount invested for 3 years
Total interest
Multiplying each by its corresponding rate
(0.02 × y) + (0.05 × (y+1000)) + (0.06 × (11000-2y)) = 600
0.02y + 0.05y + 50 + 660 - 0.12y = 600
-0.05y + 710 = 600
-0.05y = 600 - 710
-0.05y = - 110
y = 2200
Therefore first year = y = $2200
Investment for 2 years =y + 1000 = 2200 + 1000 = $3200
Investment for 3 years = 11000 - 2y = (11000 - (2*2200)) = (11000 - 4400) = $6600
An aeroplane covers a distance of 1500km in a certain time at a certain speed.After increasing the speed by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time. Find the previous speed of the aeroplane.
this is from quadratic equations CBSE grade 10
please answer ASAP
Answer:
previous speed of the aeroplane is 500 km/hr
Step-by-step explanation:
Given: Distance covered by aeroplane = 1500 km
It covers the same distance in a time which is half an hour less than the previous time if the speed is increased by 100 km/hr
To find: previous speed of the aeroplane
Solution:
Let x denotes the previous speed of the aeroplane.
Time taken by an aeroplane if speed is x km/hr = distance/speed = [tex]\frac{1500}{x}[/tex] hours
If speed is increased by 100 km/hr, new speed = (x + 100) km/hr
Time taken by an aeroplane if speed is (x + 100) km/hr = [tex]\frac{1500}{x+100}[/tex] hours
According to question,
[tex]\frac{1500}{x+100}=\frac{1500}{x}-\frac{1}{2}\\ \frac{1500}{x}-\frac{1500}{x+100}=\frac{1}{2} \\\frac{1}{x}-\frac{1}{x+100}=\frac{1}{3000}\\ \frac{x+100-x}{x(x+100)}=\frac{1}{3000}\\ x^2+100x=300000\\x^2+100x-300000=0\\[/tex]
[tex]x^2+600x-500x-300000=0\\x(x+600)-500(x+600)=0\\(x-500)(x+600)=0\\x=500\,,\,-600[/tex]
As speed can not be negative, [tex]x=-600[/tex] is rejected.
So,
previous speed of the aeroplane is 500 km/hr
Which of the following is a perfect square? 221 196 224 176 Need the answer as quick as possible
Answer:
196
Step-by-step explanation:
196 is the perfect square number, because its square root is 14.
[tex] \sqrt{196} = 14[/tex]
Q, A fruit seller buys 10 apples for Rs. 45 each from wholesale market .He packs them in a fruit basket for 40 and sells them each for 20 bakets Rs. 600 .Is it loss or gain
Answer:
It is a gain.
Step-by-step explanation:
CLEAR STATEMENT:
Given that the fruit seller buys 10 apples for 45Rs each from wholesale market.
This implies her buys them for 10 × 45Rs = 450Rs.
UNCLEAR STATEMENT:
He packs them in a fruit basket for 40 and sells them each for 20 baskets Rs. 600.
ASSUMING:
What you are trying to say is that he bought baskets for 40Rs, and sold the apples for 600Rs.
Subtracting his expenses from this value, we have
600Rs - 450Rs - 40Rs = 110Rs
Since this amount is positive, we conclude that it is a gain of 110Rs.
Find the slope of the line 25 points
y
=
9
7
x
+ 1
.
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
97
Step-by-step explanation:
y=mx+b
m= slope
y=97x+1
_____ of the basic trigonometric functions have inverse functions. None, 3, 6, 4
Answer:
6
Step-by-step explanation:
There are inverses for sine, cosine, tangent, secant, cosecant, and cotangent.
What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot)
Answer:
[tex]3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Step-by-step explanation:
To find the product :
[tex](\sqrt{3x} +\sqrt5)(\sqrt{15x} +2\sqrt{30})[/tex]
[tex]\sqrt{3x}(\sqrt{15x} +2\sqrt{30}) +\sqrt5(\sqrt{15x} +2\sqrt{30})\\\Rightarrow \sqrt{3x}\times \sqrt{15x} +\sqrt{3x}\times 2\sqrt{30} +\sqrt5 \times \sqrt{15x} +\sqrt5\times 2\sqrt{30}\\\Rightarrow \sqrt{45} \times x + 2 \sqrt{90x} + \sqrt{75x} + 2 \sqrt{150}\\\Rightarrow \sqrt{5 \times 9} \times x + 2 \sqrt{9\times 10x} + \sqrt{25 \times 3x} + 2 \sqrt{25 \times 6}\\\Rightarrow 3\sqrt5 x+ 2 \times 3 \sqrt{10x} +5\sqrt{3x} +2 \times 5 \sqrt6\\\Rightarrow 3\sqrt5 x+ 6 \sqrt{10x} +5\sqrt{3x} +10 \sqrt6[/tex]
[tex]\Rightarrow 3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Some identities used:
1. [tex](a+b)(c+d) = a (c+d) + b(c+d)[/tex]
2. [tex]\sqrt9 =3[/tex]
3. [tex]\sqrt{25} =5[/tex]
4. [tex]\sqrt x \times \sqrt x=x[/tex]
5. [tex]\sqrt a \times \sqrt b = \sqrt{ab}[/tex]
So, the solution is [tex]3\sqrt5 x+ \sqrt x (6 \sqrt{10} +5\sqrt{3}) +10 \sqrt6[/tex]
Answer:it’s b
Step-by-step explanation:
On edge
Expand and Simplify (x+7)(x+5)
Answer:
[tex]=x^2+12x+35[/tex]
Step-by-step explanation:
[tex]\left(x+7\right)\left(x+5\right)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]a=x,\:b=7,\:c=x,\:d=5\\=xx+x\cdot \:5+7x+7\cdot \:5\\=xx+5x+7x+7\cdot \:5\\=x^2+12x+35[/tex]
Solve 5 + x - 14 = x - 7
Answer:
No solution
Step-by-step explanation:
5+x-14=x-7
-9+x=x-7
2+x=x
2=0
No solution
part 4. Find the missing sides for the 30 60 90 triangles. Please show work for each
10. tan(30) = l / 6√3
l = tan(30) x 6√3
l = 6
cos(30) = 6√3 / y
y = 6√3/cos(30)
y = 12
11. tan(30) = c/30
c = 30 x tan(30)
c = 10√3
cos(30) = 27/w
w = 27/cos(30)
w = 18√3
12.
sin(60) = 36/y
y = 36/sin(60)
y = 24√3
tan(60) = 36/x
x = 36/tan(60)
x = 12√3
Answer:
10. (l, y) = (6, 12)
11. (c, w) = (9√3, 18√3)
12. (x, y) = (12√3, 24√3)
Step-by-step explanation:
Side ratios, shortest to longest, in a 30°-60°-90° triangle are ...
1 : √3 : 2
__
10. l : 6√3 : y = 1 : √3 : 2
multiply by 6
= 6 : 6√3 : 12
l = 6, y = 12
__
11. c : 27 : w = 1 : √3 : 2
multiply by 27/√3 = 9√3
= 9√3 : 27 : 18√3
c = 9√3, w = 18√3
__
12. x : 36 : y = 1 : √3 : 2
multiply by 36/√3 = 12√3
= 12√3 : 36 : 24√3
x = 12√3, y = 24√3
__
This is easier when the triangle is drawn to clearly differentiate the lengths of the sides. The long leg is opposite the 60° angle; the short leg is opposite the 30° angle.
3x+4+3=40 i need help very fast
Answer:
x = 11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
3x11 = 33
4+3 = 7
33 + 7 = 40
3. Shenker has 45 CDs.
He gives 10 CDs to his brother.
a) Write an equation you can solve to find how many CDs
Shenker has left.
b) Solve the equation.
Answer: The equation is 45-10=x the answer is 35
Step-by-step explanation: To make the equation you need to have and = sign so, we can do what he has (45) and subtract what he gives away (10) which would equal what he has left (x)
Answer:
45 (initial amount) - 10 (given to brother) = x (number of cd's left)
Equation:
45 - 10 = x
Answer:
35 CDs
Help will mark brainliest
Answer:
- 1 4/5
Step-by-step explanation:
-1 1/5 + - 3/5
Since the signs are the same, we add and take the sign
1 1/5 + 3/5
1 4/5
The sign is negative
- 1 4/5
On the number line start at - 1 1/5 and go to the left 3/5( since the sign is negative) you will end up at - 1 4/5
