Answer:
[tex]BC=71\text{ units}[/tex]
Step-by-step explanation:
Since AD is an altitude, we know that AD⊥BC by the definition of altitudes.
Then, this means that ∠ADC will be 90° by the definition of perpendicular lines. Therefore:
[tex]12x+6=90[/tex]
Solve for x. Subtract 6 from both sides and then divide by 12:
[tex]12x=84\\[/tex]
[tex]x=7[/tex]
Therefore, the value of x is 7.
BC is the addition of the segments BD and DC. In other words:
[tex]BC=BD+DC[/tex]
We already know the equations of BD and DC. Substitute:
[tex]BC=(5x-7)+(2x+29)[/tex]
Since we know that the value of x is 7, substitute 7 for x and evaluate for BC:
[tex]BC=(5(7)-7)+(2(7)+29))[/tex]
Evaluate:
[tex]BC=(35-7)+(14+29)[/tex]
Evaluate:
[tex]BC=28+43=71[/tex]
Therefore, the value of BC is 71 units.
Answer:
BC = 71
Step-by-step explanation:
12x + 6 = 90
x = 7
5x - 7 + 2x + 29 = 7x + 22
7(7) + 22 = 49 + 22
49 + 22 = 71
BC = 71
50 points pls help!!
Answer:
p = 23
q = 18
Step-by-step explanation:
The four interior angles of a square are all 90° each
4p - 2 = 90
⇒ 4p = 92
⇒ p = 92 ÷ 4
⇒ p = 23
5q = 90
⇒ q = 90 ÷ 5
⇒ q = 18
Answer:
p=23; q=18.
Step-by-step explanation:
1) m∠(XWZ)=90, then 4p-2=90 and p=23°;
2) m∠(WZY)=90, then 5q=90 and q=18°.
What value of x will make parallelogram abcd a rhombus? x =
The value of x that will make the considered parallelogram ABCD a rhombus is 4 units.
What is rhombus and some of its properties?Rhombus is a parallelogram whose all sides are of equal lengths.
Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).Its vertex angles are bisected by its diagonals.The triangles on either side of the diagonals are isosceles and congruent.For this problem, the missing figure is attached below.
We see that the angle between the diagonals is [tex](3x- 12)^\circ[/tex]
It is given that ABCD is a parallelogram.
For ABCD parallelogram to be a rhombus, its diagonals need to be perpendicular to each other.
Perpendicular lines have 90° angle between them.
Thus, we need:
[tex](3x- 12)^\circ = 90^\circ[/tex]
Evaluating value of x:
[tex](3x- 12)^\circ = 90^\circ\\3x - 12 = 90\\\text{Adding 12 on both the sides}\\3x = 102\\\text{Dividing both the sides by 3}\\\\x = 12/3 = 4[/tex]
Thus, the value of x is 4
Learn more about rhombus here:
https://brainly.com/question/1542707
Answer:
ANSWER: x=34
Step-by-step explanation:
E2020
how do you simplify 24+3x=3x+2(3•4)
Answer:
all rational numbers
Step-by-step explanation:
24+3x=3x+2(3*4) shows that there can only be two possible answer, all integers or no solution. As you can see 2*3*4 is 24, making the answer all rational numbers.
The bear population increases at a rate of 2% per year. If there are 1,200 bears currently, how many bears will there be in 10 years?
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &1200\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=\textit{elapsed time}\dotfill &10\\ \end{cases} \\\\\\ A=1200(1 + 0.02)^{10}\implies A=1200(1.02)^{10}\implies A\approx 1462[/tex]
Desperately need help
[tex]\begin{cases} x=-5\implies &x+5=0\\ x=3\implies &x-3=0 \end{cases}\qquad \implies \underline{a(x+5)(x-3)~~ = ~~\stackrel{0}{y}} \\\\\\ \stackrel{\textit{we also know that}}{P(0)=-30}\implies \begin{cases} x=0\\ y=-30 \end{cases}\implies a(0+5)(0-3)~~ = ~~-30 \\\\\\ a(5)(-3)=-30\implies -15a=-30\implies a=\cfrac{-30}{-15}\implies \boxed{a=2} \\\\[-0.35em] ~\dotfill\\\\ 2(x+5)(x-3)=y\implies 2(\stackrel{F~O~I~L}{x^2+2x-15})=y\implies \underline{2x^2+4x-30=y}[/tex]
Check the picture below.
Simplify the expression below. Show all steps.
√4x^2 ÷ 3y
Answer:
4x÷3y
Step-by-step explanation:
√4x^2 ÷ 3y
√16x÷3y
4x÷3y
Hoped it helped :)
multiply 8/2a^5 • 6/12a^2
Answer:
2/a^7
Step-by-step explanation:
what is the fractions that are multiples of 1/6
Answer:
1/31/2those would be the only onesA kite flying in the air has an 11-ft line attached to it. Its line pulled taut and casts a 9 -ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.
Step-by-step explanation:
All we have to do is apply the Pythagorean theorem which states that a²+b²=c²
where c is the hypotenuse of the triangle or the side facing the 90° angle.
Moreover a & b are the other two sides of the triangle.
[tex]11 {}^{2} = {9}^{2} + h {}^{2} [/tex]
where h is the height from the ground
[tex]121 = 81 + {h}^{2} [/tex]
[tex]h {}^{2} = 121 - 81[/tex]
[tex]h {}^{2} = 40[/tex]
[tex]h = \sqrt{40} = 6.324[/tex]
Rounding to the nearest tenth,
[tex]h = 6.3[/tex]
please help its for algebra 1
Answer:
(-1, -6)
Step-by-step explanation:
If you do rise over run you get the same slope as 8x+7y=-50
what is the image of (-2, -5) after a reflection over the line y = x
Answer:
2, -5
Step-by-step explanation:
Answer:
(-5, -2)
Step-by-step explanation:
Rule for reflection over y = x :
(x, y) -> (y, x)
I’m just a bit confuse on 16. Can someone help me T__T
Answer:
40 degrees
Step-by-step explanation:
m<3 = m<4
2x=80
x=40 degrees
Write an equation of the line passing through (-4,7) and having slope - 5. Give the answer in slope-intercept form.
The equation of the line in slope-intercept form is
Answer:
Step-by-step explanation:
The general equation is y = mx + b
You already have m which is the slope. So the general equation becomes y = -5x + b
The point is meant to find b
x = - 4
y = 7
7 = - 5*-4 + b
7 = 20 + b Subtract 20 from both sides.
7 - 20 = 20-20 + b Combine
- 13 = b
Answer: y = - 5x - 13
How do I do this and what is the correct answer?
Answer:
10 2/3
Step-by-step explanation:
[tex] \frac{24}{9} = \frac{8}{3} [/tex]
[tex] \frac{8}{3} + 8 = \frac{8 + 24}{3} = \frac{32}{3} = 10 \frac{2}{3} [/tex]
help with question pls I don't understand
Answer:
15x^3y+6x^2y^2+9xy^3
Step-by-step explanation:
3xy ( 5x^2 +2xy +3y^2)
Distribute the 3xy to all terms in the parentheses
3xy*5x^2+3xy*2xy+3xy*3y^2
15x^3y+6x^2y^2+9xy^3
Answer:
15[tex]x^{3}[/tex]y + 6[tex]x^{2}[/tex][tex]y^{2}[/tex] + 9x[tex]y^{3}[/tex]
Step-by-step explanation:
multiple everything in the brackets by 3xy
3xy x 5[tex]x^{2}[/tex] = 15[tex]x^{3}[/tex]y
3xy x 2xy = 6[tex]x^{2}[/tex][tex]y^{2}[/tex]
3xy x 3[tex]y^{2}[/tex] = 9x[tex]y^{3}[/tex]
15[tex]x^{3}[/tex]y + 6[tex]x^{2}[/tex][tex]y^{2}[/tex] + 9x[tex]y^{3}[/tex]
The are of a circle is 109.4cm^2. Calculate the length of its radius.
Answer:
r≈ 5.9 cm
Step-by-step explanation:
isosceles and equilateral
Answer:
I think it is 60°
Step-by-step explanation:
b/c angle of triangle is 180° and when we divide 180° by 3 it will be 60°
In the following pictograph, how many total books have the four groups read?
a. 27
b. 90
c. 54
d. 9
Best answer gets brainliest!
Answer:
c; 54
Step-by-step explanation:
to find the answer you can first add all the books together
this can be represented by
3 + 2 + 2.5 + 1.5
this answer is 9
then multiply it by 6
9 * 6 = 54
is is c
Solve the compound inequality.
7
Answer:
Ok, first of all, that's not an inequlity. An inequality includes < or >, and also ≤ or ≥. 7 is not an inequality, so perhaps you made a mistake typing the question?
Step-by-step explanation:
Solve for all possible values of x : |x-3|+4=1
A: 6
B: 0
C: 6 or 0
D: no real solutions
Answer:
D: no real solutions
Step-by-step explanation:
Please show steps to answer. No links please
Answer:
18 hours after 10 AM
Step-by-step explanation:
We are looking for the time the helicopter and the plane will be the same distance from Burbank after 10 AM.We are given the two equations for the distance that the helicopter and the plane are away, in miles.It also says that R is the variable for time.Using this information, we need to solve for the time with broth equations, so we would set both up to be equal to each other, since they will be the same distance away from each other.It would look like this: -150r + 260 = -270r + 440.Add 150r to both sides.260 = -10r + 440.Add -10r to both sides.Now we have 10r + 260 = 440Subtract 260 from both sides.10r = 180Divide each side by 10 to isolate the R.R = 18.It would be 18 hours after 10 AM.If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
(2)/(3)a-7+(7)/(18)a-5(1)/(6)
Answer:
19a - 141
-------------
18
Step-by-step explanation:
Combine multiplied terms into a single fraction
Combine multiplied terms into a single fraction
Multiply the numbers
Help please???????????
Answer:
525
Step-by-step explanation:
i really dont know what it asking
How long will it take to count to 3,140,000 by 1's?
show you work!
explain your answer!
Answer:
A long time
Step-by-step explanation:
A long time
help me please I don't understand
Answer:
it is B. increasing
Answer:
C.it is a constant
Step-by-step explanation:
Hope this helped!
Please mark me as brainliest!
Which of the following probabilities is equal to approximately 0.2957? use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 0.50 0.6915 0.75 0.7734 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 p (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.25) p (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.75) p (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25) p (0.75 less-than-or-equal-to z less-than-or-equal-to 1.25)
A z-table is also known as the standard normal distribution table. The probability of P(0.75≤ z ≤ 1.25) is 0.121.
What is a Z-table?A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
As it is given that the probability and the z-table is given to us, as shown below,
z Probability
0.00 0.5000
0.25 0.59871
0.50 0.6915
0.75 0.7734
1.00 0.8413
1.25 0.8944
1.50 0.9332
1.75 0.9599
The following probabilities can be written as:
1. The probability of P(-1.25)
[tex]P(-z)=1-P(z)\\\\P(-1.25)=1-P(1.25)\\\\P(-1.25)=1-(0.8944)\\\\P(-1.25)=0.1056[/tex]
The probability of P(-1.25) is 0.1056.
2. The probability of P(-1.25 ≤ z ≤ 0.25)
[tex]P(-1.25\leq z\leq 0.25)=P(0.25)-P(-1.25)\\\\P(-1.25\leq z\leq 0.25)=0.59871-0.1056=0.49311[/tex]
The probability of P(-1.25 ≤ z ≤ 0.25) is 0.49311.
3. The probability of P(-1.25 ≤ z ≤ 0.75)
[tex]P(-1.25\leq z\leq 0.75)=P(0.75)-P(-1.25)\\\\P(-1.25\leq z\leq 0.75)=0.7734-0.1056=0.6678[/tex]
The probability of P(-1.25 ≤ z ≤ 0.75) is 0.6678.
4. The probability of P(0.25 ≤ z ≤ 1.25)
[tex]P(0.25 \leq z\leq 1.25)=P(1.25)-P(0.25)\\\\P(0.25\leq z\leq 1.25)=0.8944-0.59871=0.29569[/tex]
The probability of P(0.25 ≤ z ≤ 1.25) is 0.29569.
5. The probability of P(0.75≤ z ≤ 1.25)
[tex]P(0.75\leq z\leq 1.25)=P(1.25)-P(0.75)\\\\P(0.75\leq z\leq 1.25)=0.8944-0.7734=0.121[/tex]
The probability of P(0.75≤ z ≤ 1.25) is 0.121.
Learn more about Z-table:
https://brainly.com/question/6096474
Answer:
C
Step-by-step explanation:
P (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25)
A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. the authors of the study wanted to know if the two groups of teachers had different levels of job satisfaction. they will use a significance level of 5% for their test. upper-tail values a 5% 2.5% 1% critical z-values 1.65 1.96 2.58 what is (are) the critical value(s) for z in this study? –1.65 and 1.65 –1.96 and 1.96 1.65 1.96
The critical values of Z in this study are given by: Option C: -1.96 and 1.96
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
For this case, we want to know if the two groups of teachers had different levels of job satisfaction.
Suppose that we have:
[tex]\mu_1[/tex] = mean of level of job satisfaction for first group of teachers.[tex]\mu_2[/tex] = mean of level of job satisfaction for second group of teachers.Then, as the test is for checking if the difference exist, the null hypothesis will deny existence of any difference.
Thus, we get:
Null hypothesis: [tex]H_0: \mu_1-\mu_2 = 0[/tex] or we say [tex]H_0: \mu_1 = \mu_2[/tex]Alternate hypothesis: [tex]H_1: \mu_1-\mu_2 \neq 0[/tex] or we say [tex]H_1: \mu_1 \neq \mu_2[/tex]The alternate hypothesis creates two regions, on either side as:
[tex]\mu_1 < \mu_2[/tex] and [tex]\mu_1 > \mu_2[/tex]
This is why it is two tailed test.
The level of significance is 5% specified.
Thus, [tex]\alpha = 5\% = 5/100 = 0.05[/tex]
From the critical values table, the critical value(s) of Z for level of significance 0.05 and for two tailed test are: [tex]\pm 1.96[/tex]
Thus, the critical values of Z in this study are given by: Option C: -1.96 and 1.96
Learn more about hypothesis testing here:
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Answer:
Step-by-step explanation:
its option B
a practice field is 250 feet long . the game field is 40% longer than the practice field . how long is the game field
The game field is 350 40 percent for 250 is 100 and 250 plus 100 is 350
Find the sum of 3squared4 and 2 squared 3 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answer:
1
Step-by-step explanation:
you gotta add
PLEASE HELP!
subtract [tex]\frac{3p}{5}[/tex] - [tex]\frac{1}{6}[/tex]
Answer:
Your answer is: 18p-5/30
To subtract fractions, find the LCD and then combine.
Step-by-step explanation:
Hope this helped : )
Answer:
---------------------------------answer will be (18p-5)/30_____________________