Answer:
[tex] \displaystyle x = 15[/tex]
Step-by-step explanation:
by triangle midsegment theorem we obtain:
[tex] \displaystyle \frac{10x + 44}{2} = 8x - 23[/tex]
simplify division:
[tex] \displaystyle 5x + 22 = 8x - 23[/tex]
move 5x to right hand side and -23 to the left hand side and change its sign:
[tex] \displaystyle 22 + 23= 8x - 5x[/tex]
simplify addition:
[tex] \displaystyle 8x - 5x = 45[/tex]
collect like terms:
[tex] \displaystyle 3x = 45[/tex]
divide both sides by 3:
[tex] \displaystyle x = 15[/tex]
and we are done!
if f(x) = 2X -5 and g(x)=x^2-8 find (f+g)(x)
Answer:
im not dure
Step-by-step explanation:
a rectangular lawn of dimensions 6x metres by x metres. In the centre is a rectangular flower bed of length (x + 4) m and width (x - 1) m. If the area of the shaded region is 40 m’, calculate the area of the flower bed.
Answer:
The area of flower bed is 8.96 m^2.
Step-by-step explanation:
Length of lawn = 6 x
width of lawn = x
length of flower bed = x + 4
width of flower bed = x - 1
Area of shaded region = 40 m^2
Area of the shaded region
6 x (x) - (x +4)(x -1) = 40
[tex]5 x^2 - 3 x - 36 = 0 \\\\x = \frac{-3\pm\sqrt{9 + 720}}{10}\\\\x = \frac{-3\pm 27}{10}=2.4 m, - 3 m[/tex]
As length cannot have negative value, so x = 2.4 m.
Area of flower bed = (x + 4)(x - 1) = (2.4 + 4)(2.4 - 1) = 8.96 m^2
Helen draws a random circle
she then measures it diameter
Answer:
Lower Bound = 2.996
Upper bound = 3.244
Step-by-step explanation:
what equation do I use to find the apothem?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Help me this is due soon
Answer:
It's (-1.5,-5.5)
Step-by-step explanation:
Answer:
-1.5 , -5.5
Step-by-step explanation:
In a certain arithmetic sequence, if -4 is the first term and 10 is the third term, which term is 157?
Answer:
a₁₅₇ = 1,088
Step-by-step explanation:
aₙ = a₁ + d(n-1); where 'd' if common difference
a₁₅₇ = -4 + 7(156)
= -4 + 1092
= 1,088
Answer:
157 is the 24th term
Step-by-step explanation:
The formula for arithmetic sequences is an=a1+(n-1)d,
where an is the nth term, a1 is the first term, n is the term position, and d is the common difference
First, we need to find the common difference using the 10.
Since it's the third term, we have 10=-4+(3-1)d
Solving for d gives us d=7
Next, we need to find the term number of 157
Thus, we have 157=-4+(n-1)*7
Solving for n gives us n=24
We can check it like this: Following order of operations (i.e. PEMDAS) gives us 24-1=23*7=161-4=157
What is the solution to the system of linear equations?
Step-by-step explanation:
is connected to graph before u learn this u must know your graph
Two amounts of money are in the ratio 8:3 if the second amount is 4.05,what is the value if the first amount?
Answer: 10.75 currency units
Step-by-step explanation:
The amounts of money are in the ration 8:3 which means that for every 3 units of the second amount, there are 8 units of the first.
Use direct proportion to solve:
8 : 3
x ; 4.03
Cross multiply to get:
3x = 32.24
x = 32.24 / 3
x = 10.75 currency units
58:36
If Zöe orders a book from Store Y, how much tax will she pay?
Comparison of Online Bookstores
Store X
Store Y
Cost of book
$17.00
$18.00
Tax rate
6%
8%
Shipping
10% of cost before tax
FREE
$1.44
$2.25
O $12.25
O $14.40
Answer:
$1.44
Step-by-step explanation:
Tax is a compulsory sum levied by the government. it increases the price of the good
tax paid = tax rate x price of the book
18 x 8%
18 x 0.08 = $1.44
If 0(0,0), B(5,0) and C(5,5) are three points. Prove that
OB=OC.
Step-by-step explanation:
you must have written something wrong.
because given that information OB is not equal to OC.
but for example, OB = BC.
the distance of OB is (5,0) - (0,0) = (5-0,0-0) = (5,0) =
= sqrt(5² + 0²) = sqrt(25) = 5
the distance of OC is (5,5)-(0,0) = (5-0,5-0) = (5,5) =
= sqrt(5² + 5²) = sqrt(50) = 5×sqrt(2)
so, OB is NOT the same as OC.
but BC is (5,5)-(5,0) = (5-5,5-0) = (0,5) = sqrt(0² + 5²) =
= sqrt(25) = 5
Find the area of this triangle.
Round to the nearest tenth.
7 m
125°
14 m
?] m2
Enter
Answer:
40.1
Step-by-step explanation:
i just did it and got it right
Alex bought 2 printer cartridges for $28 each and a printer for $85. He gave the cashier $150. How much change should Alex have received from the cashier?
Answer:
$9 in change
Step-by-step explanation:
Find the total cost of his purchases:
28 + 28 + 85
= 141
Find how much change he received by subtracting this from 150:
150 - 141
= 9
So, he should have received $9 in change
Help me I don't know any
Answer:
25%
Step-by-step explanation:
(a)
We need to express in percent 8 as a percent of 32.
We have,
Numerator = 8
Denominator = 32
Percent,
[tex]P=\dfrac{8}{32}\times 100\\\\=25\%[/tex]
Hence, the required percentage is 25%.
PLEASE I NEED THE ANSWER WITH THE EXPLANATION DON'T IGNORE MY QUESTION!!!
The
mean of six numbers is 12.five of the numbers
are 11,7,21,14 and 9. calculate the sixth number.
The answer is attached. I hope this helps answer your question!
Answer:
10
Step-by-step explanation:
data=11,7,21,14,9,x
mean=sum of data/no of data
12=11+7+21+14+9+x/6
12*6=62+x
72-62=x
10=x
therefore sixth number is 10.
i need helppp helpp me pleaseeeee!!
Answer:
y = 6
Step-by-step explanation:
Answer:
i helped
Step-by-step explanation:
the sum of 43.9 and 4 groups of a number
Answer:
10.975+10.975+10.975+10.975
Step-by-step explanation:
Find the range and the interquartile range of the given data set.
2, 4, 7, 8, 16, 19, 21
Michael has 2 hats, 3 shirts, and 8 pants. How many different ways can he wear the outfits if he wears one of each?
Answer:
2
Step-by-step explanation:
The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the number of milligrams of the substance and t represents the time. In years. In the function p(t), explain what 0.25 and 500 represent.
Given:
The function is:
[tex]p(t)=500(0.25)^t[/tex]
Where p(t) represents the number of milligrams of the substance and t represents the time.
To find:
The correct explanation for the number 0.25 and 500 in the given function.
Solution:
The general exponential function is:
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth/decay factor. If [tex]0<b<1[/tex], then decay factor and if [tex]b>1[/tex], then growth factor.
We have,
[tex]p(t)=500(0.25)^t[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=500[/tex], it means initial there are 500 milligrams of the substance.
[tex]b=0.25[/tex], this value is less than 1, it means the substance is decreasing by a factor of 0.25.
Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.
Round 31.24 to 1 decimal place
Round 5.275 to 2 decimal place
Round 0.56489 to 3 decimal place
Answer:
1. 31.2
2. 5.28
3. 0.565
Step-by-step explanation:
Remember if the number is 1-4 round down and if the number is 5-9 round up.
Hope this is helpful
#happylearning
Find the missing side of the triangle. Round your answers to the nearest tenth if necessary.
12.4 in
3.1 in
16.7 in
11.2 in
Answer:
3.1 in
Step-by-step explanation:
a² + b² =c²
12=c
11.6=b
c²- b² = a²
12²-11.6²= 9.44
√9.44 = 3.07 Rounded = 3.1 in
Here are the equations of two different graphs: y = x-7 and y = 3x - 7 Are the gradients of the graphs the same or different? Explain how you know.
help please
Answer:
this two graph is not same because they have different slopes for this they are not same
please help meeeeeeee
https://youtu.be/QnydfcNVJoQ
sypport my channel pls pls
channel name sabrina clodia
Answer:
x + y = 60
Step-by-step explanation:
[tex]2x + 2y + 60 = 180 \\ 2x + 2y = 180 - 60 \\ 2x + 2y = 120 \\ \frac{2x + 2y}{2} = \frac{120}{2} \\ x + y = 60 \\ [/tex]
which of these points lies on the circle with center (2 3) and radius 2
A. (4,3)
B. (3,4)
C. (-1,0)
D. (1,3)
Answer:
A. 4,3
Step-by-step explanation:
that's it thanks brainliest please
Answer:
A) (4,3)
Step-by-step explanation:
Move triangle ABC so it lies on top of triangle DEF, triangle GHI, and triangle JKL. How many units do you have to move triangle ABC from its original location to coincide with each of the other triangles? Specify how triangle ABC moves up, down, left, or right.
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the diagram of coordinates of the three triangles are not given.
A general explanation is as follows:
First, record the coordinates of the corresponding points of the three triangles.
For instance; In triangles ABC, DEF and GHI; A, D and G are corresponding points.
Now, assume the coordinates are:
[tex]A = (1,1)[/tex]
[tex]D = (1,5)[/tex]
[tex]G= (-2,1)[/tex]
Point D is 4 points to the right of A;
i.e.
[tex]D =(1,1+4) = (1,5)[/tex]
Hence, ABC will be moved 4 units right to lie on DEF
Similarly, point G is 3 units down of A
i.e.
[tex]G =(1-3,1) = (-2,1)[/tex]
Hence, ABC will be moved 3 units down to lie on GHI.
Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Selext three options.
Answer:
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
The transformation is rigid.
Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
If figure 1 is located 360° about point C, it will be mapped onto itself.
Step-by-step explanation:
Anca rolls two number cubes labelled 3 to 8. She adds the numbers that show on the cubes. List the possible outcomes. b) What is the probability of getting '13'? c) What is the probability of getting '21'? d) What result should occur the most?
Answer:
Find the theoretical probability that you will choose each color. P(green) = ___/___ ... 98% or 100%. 3. Bailey uses the results from an experiment to calculate the probability of each color of block being chosen from a bucket. He ... If the sum of the two number cubes in even, Player 1 (or) 2 scores a point.
Step-by-step explanation:
A city has 18 radio stations, including 4 college radio stations.
What is the probability that a randomly chosen radio station in this city is a college radio
station?
Write your answer as a fraction or whole number.
Answer:
2/9
Step-by-step explanation:
P=4/18=2/9
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Ahmed paid $34 000 for a car. His car decreased in value by 40% at the end of the first year. The value at the end of the second year was 10% less than the value at the end of the first year. . Calculate the value of Ahmed's car after 2 years .
40% of 34 000
40/100 * 34 000 = 13 600
subtract : 34000 - 13 600 = 20 400
Second step:10% of 20 400
10/100 * 20 400 = 2040
subtract : 20 400 - 2040 = $ 18 360
Final Answer = $ 18 360what is 2/3 of 4 hours and 30 minutes?